# The set S_n weight enumerated by # t^(# of copies of 132) for n up to, 18 L18:=[1, 2, 5+t, 14+4*t^2+5*t+t^3, 42+14*t^3+23*t^2+12*t^4+3*t^6+21*t+5*t^5, 132+84* t+107*t^2+82*t^3+96*t^4+64*t^6+55*t^5+22*t^9+37*t^7+29*t^8+10*t^10+2*t^12, 429+ 330*t+464*t^2+410*t^3+526*t^4+475*t^6+394*t^5+298*t^9+365*t^7+360*t^8+281*t^10+ 206*t^12+126*t^13+55*t^15+13*t^18+175*t^11+93*t^14+14*t^17+23*t^16+2*t^20+t^19, 1430+1287*t+1950*t^2+1918*t^3+2593*t^4+2858*t^6+2225*t^5+2401*t^9+2489*t^7+2682 *t^8+2620*t^10+2321*t^12+1853*t^13+1576*t^15+1048*t^18+2088*t^11+1770*t^14+1152 *t^17+1417*t^16+647*t^20+730*t^19+162*t^24+397*t^21+322*t^22+109*t^25+37*t^27+7 *t^30+169*t^23+41*t^26+20*t^28+t^31, 4862+5005*t+8063*t^2+8657*t^3+12165*t^4+ 15174*t^6+11539*t^5+16066*t^9+14772*t^7+16627*t^8+18248*t^10+18449*t^12+16681*t ^13+16300*t^15+14891*t^18+16413*t^11+17104*t^14+14486*t^17+16525*t^16+12952*t^ 20+12878*t^19+8484*t^24+11213*t^21+10816*t^22+7136*t^25+4914*t^27+2722*t^30+ 8969*t^23+6163*t^26+4110*t^28+6*t^43+t^46+11*t^41+107*t^38+950*t^34+311*t^37+ 141*t^39+37*t^42+509*t^35+5*t^45+3094*t^29+1181*t^33+1611*t^32+510*t^36+85*t^40 +1937*t^31, 16796+19448*t+33033*t^2+38225*t^3+55482*t^4+76381*t^6+57064*t^5+ 96248*t^9+79768*t^7+94243*t^8+112709*t^10+124827*t^12+121352*t^13+129704*t^15+ 137479*t^18+109422*t^11+130154*t^14+130013*t^17+137826*t^16+134624*t^20+129923* t^19+120597*t^24+128037*t^21+129817*t^22+112847*t^25+101464*t^27+86333*t^30+ 119910*t^23+109851*t^26+98255*t^28+t^64+11*t^61+4*t^62+26*t^59+83*t^58+562*t^54 +159*t^57+6*t^63+271*t^55+44*t^60+1584*t^51+681*t^53+2658*t^49+10735*t^44+4158* t^48+1040*t^52+175*t^56+5023*t^47+2056*t^50+12781*t^43+6665*t^46+18854*t^41+ 31539*t^38+57142*t^34+36867*t^37+26333*t^39+16276*t^42+47504*t^35+8453*t^45+ 88302*t^29+62466*t^33+71042*t^32+43980*t^36+23803*t^40+75684*t^31, 58786+75582* t+134576*t^2+166322*t^3+248509*t^4+372506*t^6+273612*t^5+540405*t^9+411132*t^7+ 501367*t^8+645884*t^10+771103*t^12+792470*t^13+904364*t^15+1062388*t^18+666591* t^11+873391*t^14+984496*t^17+988292*t^16+1121118*t^20+1058312*t^19+1182129*t^24 +1117511*t^21+1167522*t^22+1158052*t^25+1150418*t^27+1134523*t^30+1140122*t^23+ 1180398*t^26+1167814*t^28+26314*t^64+50919*t^61+41128*t^62+73269*t^59+90914*t^ 58+170845*t^54+104648*t^57+32514*t^63+144866*t^55+62680*t^60+251343*t^51+190755 *t^53+316887*t^49+541746*t^44+365025*t^48+226338*t^52+126540*t^56+396602*t^47+ 287377*t^50+583310*t^43+449094*t^46+684351*t^41+839814*t^38+1008723*t^34+874695 *t^37+777886*t^39+647464*t^42+948246*t^35+487788*t^45+1120075*t^29+1022688*t^33 +1075062*t^32+933609*t^36+749612*t^40+1080774*t^31+t^87+6*t^83+6*t^85+4*t^86+41 *t^82+82*t^81+150*t^79+343*t^78+111*t^80+3647*t^71+769*t^76+19*t^84+12085*t^67+ 1284*t^74+7079*t^69+358*t^77+2099*t^73+9197*t^68+2884*t^72+16651*t^66+5386*t^70 +19986*t^65+1016*t^75, 208012+293930*t+546312*t^2+716170*t^3+1099255*t^4+ 1778065*t^6+1283621*t^5+2891450*t^9+2056005*t^7+2574201*t^8+3533411*t^10+ 4496459*t^12+4816550*t^13+5813312*t^15+7407256*t^18+3819011*t^11+5442384*t^14+ 6736605*t^17+6493101*t^16+8275941*t^20+7664364*t^19+9776268*t^24+8526536*t^21+ 9108397*t^22+9911016*t^25+10443362*t^27+11187440*t^30+9242454*t^23+10342283*t^ 26+10852806*t^28+2945167*t^64+3813548*t^61+3528252*t^62+4486183*t^59+4896812*t^ 58+6451607*t^54+5213842*t^57+3192510*t^63+5988665*t^55+4191364*t^60+7575442*t^ 51+6768796*t^53+8331411*t^49+10028728*t^44+8782122*t^48+7269234*t^52+5664110*t^ 56+9011096*t^47+8037308*t^50+10180653*t^43+9459865*t^46+10617021*t^41+11226970* t^38+11458030*t^34+11221173*t^37+10963400*t^39+10553059*t^42+11285094*t^35+ 9652288*t^45+10824365*t^29+11266034*t^33+11371095*t^32+11429456*t^36+10956799*t ^40+11127849*t^31+90255*t^87+201318*t^83+138763*t^85+112423*t^86+252875*t^82+ 297731*t^81+422342*t^79+505321*t^78+357247*t^80+1348904*t^71+694716*t^76+171058 *t^84+2150851*t^67+917150*t^74+1723618*t^69+582928*t^77+1051282*t^73+1948015*t^ 68+1213585*t^72+2415683*t^66+1553586*t^70+2633502*t^65+793302*t^75+80*t^107+ 1739*t^101+6936*t^97+14*t^112+1178*t^102+636*t^103+612*t^104+137*t^108+4536*t^ 98+26718*t^92+57130*t^89+3233*t^99+16589*t^94+471*t^105+34750*t^91+9260*t^96+ 72077*t^88+11364*t^95+2739*t^100+21915*t^93+47392*t^90+5*t^113+10*t^111+203*t^ 106+58*t^109+4*t^114+33*t^110+t^115, 742900+1144066*t+2212550*t^2+3059864*t^3+ 4817998*t^4+8354138*t^6+5924924*t^5+15011008*t^9+10060493*t^7+12897207*t^8+ 18673681*t^10+25139809*t^12+27892921*t^13+35371892*t^15+48216406*t^18+21005742* t^11+32174765*t^14+43156127*t^17+40213111*t^16+56507678*t^20+51435788*t^19+ 73131496*t^24+59835060*t^21+65040250*t^22+76159482*t^25+83886770*t^27+95617414* t^30+68003213*t^23+80950418*t^26+88704466*t^28+85349463*t^64+94730489*t^61+290* t^138+22*t^143+192*t^139+92050979*t^62+100671135*t^59+104095864*t^58+113498686* t^54+106018365*t^57+88207742*t^63+110736720*t^55+98411555*t^60+117641966*t^51+ 114487535*t^53+119890161*t^49+122191448*t^44+121539559*t^48+117068552*t^52+ 109185266*t^56+121107517*t^47+119647471*t^50+120873012*t^43+122437895*t^46+ 119115467*t^41+116077044*t^38+107441769*t^34+113400805*t^37+116689240*t^39+ 121162775*t^42+108837186*t^35+121514118*t^45+91012203*t^29+103634743*t^33+ 101831844*t^32+112303428*t^36+119170110*t^40+97782285*t^31+18497133*t^87+ 26345986*t^83+22217570*t^85+55*t^142+20399148*t^86+28875704*t^82+31049684*t^81+ 36180550*t^79+39122434*t^78+33743546*t^80+60572473*t^71+44965351*t^76+24411447* t^84+74484430*t^67+51090362*t^74+67472416*t^69+41689056*t^77+54027243*t^73+ 71353679*t^68+57665260*t^72+78416747*t^66+64445251*t^70+81309503*t^65+47689672* t^75+1381705*t^107+86*t^141+7*t^146+3505157*t^101+6061409*t^97+570400*t^112+ 3066630*t^102+2625069*t^103+2261232*t^104+1182413*t^108+5353769*t^98+11107776*t ^92+15146327*t^89+4643145*t^99+8843444*t^94+1933181*t^105+12330777*t^91+6931018 *t^96+16888832*t^88+7773620*t^95+4078991*t^100+9870538*t^93+13796919*t^90+ 461542*t^113+681977*t^111+1641478*t^106+988179*t^109+388862*t^114+832910*t^110+ 309683*t^115+t^147+10*t^145+26*t^144+1452*t^134+3706*t^132+550*t^137+956*t^136+ 14885*t^127+2250*t^133+8675*t^129+35468*t^124+1270*t^135+161513*t^118+7065*t^ 130+45715*t^123+224*t^140+11762*t^128+61659*t^122+204198*t^117+123151*t^119+ 254253*t^116+83051*t^121+29909*t^125+4355*t^131+103938*t^120+22444*t^126, 2674440+4457400*t+8946454*t^2+12994936*t^3+20968680*t^4+38773898*t^6+27005978*t ^5+76218029*t^9+48415037*t^7+63440820*t^8+96416035*t^10+136409188*t^12+ 155815422*t^13+206518151*t^15+299044137*t^18+112042054*t^11+183244691*t^14+ 263430595*t^17+238823705*t^16+365202261*t^20+327050513*t^19+511067038*t^24+ 395649155*t^21+436990924*t^22+544131658*t^25+621916279*t^27+746501992*t^30+ 467967476*t^23+587718014*t^26+667606694*t^28+5*t^185+1395961785*t^64+1416636271 *t^61+6687374*t^138+2873233*t^143+5689279*t^139+1415165681*t^62+1423771577*t^59 +1430505782*t^58+1412713381*t^54+1423209185*t^57+1401135684*t^63+1414476476*t^ 55+1426997850*t^60+1371904468*t^51+1396532373*t^53+1339596996*t^49+1233205989*t ^44+1327079063*t^48+1391984488*t^52+1425768690*t^56+1299554183*t^47+1362658567* t^50+1199577490*t^43+1284033503*t^46+1139325459*t^41+1047691505*t^38+902033896* t^34+1006993331*t^37+1075327133*t^39+1176886741*t^42+933069794*t^35+1252872951* t^45+700378580*t^29+857167165*t^33+824717276*t^32+976957712*t^36+1115184505*t^ 40+779883891*t^31+765030984*t^87+899655863*t^83+832335142*t^85+3453881*t^142+15 *t^183+196*t^178+298*t^177+979*t^174+800931190*t^86+937165691*t^82+967324488*t^ 81+1033588520*t^79+1069389739*t^78+1003909299*t^80+1265202324*t^71+1132532886*t ^76+869015071*t^84+1347964603*t^67+1190943112*t^74+1309984314*t^69+1097410370*t ^77+1214837532*t^73+1334427647*t^68+1245216145*t^72+1369033505*t^66+1293411020* t^70+1377882835*t^65+1158172695*t^75+230455948*t^107+4085133*t^141+1672777*t^ 146+355045203*t^101+456993055*t^97+152708335*t^112+333158612*t^102+309832979*t^ 103+289558065*t^104+213785483*t^108+431540488*t^98+604965623*t^92+698475928*t^ 89+404097111*t^99+544199998*t^94+268364768*t^105+634442907*t^91+486090504*t^96+ 734193065*t^88+512793264*t^95+380541053*t^100+572321903*t^93+668549432*t^90+27* t^182+139026271*t^113+123*t^179+12*t^184+50*t^181+3*t^186+165979626*t^111+ 249842278*t^106+196509300*t^109+127400917*t^114+181398289*t^110+115514450*t^115 +1379254*t^147+2019653*t^145+2431972*t^144+12250911*t^134+16280009*t^132+ 7776095*t^137+9139394*t^136+31178607*t^127+14077783*t^133+24204105*t^129+ 44845464*t^124+10558376*t^135+86238629*t^118+21339593*t^130+50096017*t^123+ 4844832*t^140+27599287*t^128+56272801*t^122+95024818*t^117+77352084*t^119+ 105186018*t^116+62667498*t^121+39721228*t^125+18553958*t^131+69995456*t^120+ 35370019*t^126+2243*t^172+10226*t^167+327342*t^154+775*t^175+127409*t^158+4570* t^170+34447*t^163+102*t^180+98529*t^159+20841*t^165+3055*t^171+78301*t^160+ 15965*t^166+505630*t^152+61095*t^161+921671*t^149+254973*t^155+769407*t^150+ 403978*t^153+1150141*t^148+618649*t^151+207251*t^156+166701*t^157+47189*t^162+ 8404*t^168+511*t^176+1432*t^173+5815*t^169+26397*t^164, 9694845+17383860*t+ 36134656*t^2+54924212*t^3+90747564*t^4+178195562*t^6+121861262*t^5+380309977*t^ 9+229917706*t^7+307570163*t^8+489000503*t^10+723034529*t^12+847533350*t^13+ 1169155763*t^15+1787371342*t^18+584558237*t^11+1014163699*t^14+1551434496*t^17+ 1373175798*t^16+2264580989*t^20+1997899742*t^19+3396130740*t^24+2503727803*t^21 +2805163754*t^22+3686200356*t^25+4352386721*t^27+5466078702*t^30+3066564931*t^ 23+4038955795*t^26+4735587327*t^28+5828833*t^185+17344353430*t^64+16714103390*t ^61+1739680321*t^138+1161112728*t^143+1607140549*t^139+16967898903*t^62+ 16239634298*t^59+16026509612*t^58+14845196113*t^54+15708268157*t^57+17121421962 *t^63+15119265681*t^55+16528382483*t^60+13786024293*t^51+14472589051*t^53+ 13059807294*t^49+11144241319*t^44+12725252279*t^48+14181061650*t^52+15463421155 *t^56+12297078493*t^47+13468510190*t^50+10697527017*t^43+11949838957*t^46+ 9869690633*t^41+8665092004*t^38+7025686265*t^34+8217482693*t^37+9042347456*t^39 +10325207051*t^42+7392983822*t^35+11507815598*t^45+5061916252*t^29+6589662701*t ^33+6230832517*t^32+7840273722*t^36+9499051741*t^40+5813452002*t^31+968*t^219+ 16344768446*t^87+17198489840*t^83+16806364793*t^85+1265221800*t^142+8318871*t^ 183+18992818*t^178+22135886*t^177+34885701*t^174+16613122792*t^86+17407958951*t ^82+17525869732*t^81+17781567087*t^79+17916932069*t^78+17697297090*t^80+ 18051421043*t^71+18063932894*t^76+17044024844*t^84+17735764923*t^67+18129816291 *t^74+17930902115*t^69+17961560752*t^77+18098863253*t^73+17883313603*t^68+ 18124573461*t^72+17650122330*t^66+18043518263*t^70+17461529935*t^65+18067043486 *t^75+9723164943*t^107+1370371239*t^141+897178944*t^146+11891118453*t^101+ 13309467773*t^97+7991219847*t^112+11551676394*t^102+11168627936*t^103+ 10825089905*t^104+9383593141*t^108+12983053685*t^98+14979815075*t^92+ 15823046246*t^89+12607017653*t^99+14346108830*t^94+10443861585*t^105+ 15255274076*t^91+13676088413*t^96+16122930074*t^88+13987508941*t^95+12273784915 *t^100+14640103444*t^93+15574263465*t^90+9819179*t^182+7640502825*t^113+ 16091798*t^179+7019802*t^184+11617115*t^181+4898837*t^186+8317025506*t^111+ 10101369248*t^106+9013917529*t^109+7323886601*t^114+8678414658*t^110+6987672333 *t^115+819020626*t^147+978610549*t^145+1069022604*t^144+2335841682*t^134+ 2683346604*t^132+1873079024*t^137+2022531577*t^136+3693756598*t^127+2500949085* t^133+3261373191*t^129+4414348111*t^124+2171087077*t^135+6068452209*t^118+ 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