#OK to post homework
#Tianyi Liu, Nov22, Assignment 20

1.
i. 
for 100 element, it would be 0.
for 101 element, it would be 353756434002780310839195762053340919620964254979217839760460653971144950604657889280
for 99 element, it would be 7219420626374262015735816679828665771084801962923738489040964199989740473222840320
ii.
23792695638183628316167125166708722722054741318989995555688894753342022292474103758734144789060946967960716668504295*ln(e)^100
iii.
It is beyond computer's computational ability
coeff(taylor(add((e^x-1-x^2/2!-x^5/5!)^(2*i+1)/(2*i+1)!,i=0..50),x=0,101),x,100)*100!

2.
i.
for 100 element, it would be 0
for 99 element, it would be 712829143817085105474623215378994077497176405077762658252232547806200878775835886248718154051954492291534316084944812283913710506546492656844800000000000000
for 101 element, it would be 7417194532958891110129008188929669157142969071229433434917402091436480223544424741563691009067011753781394069807995438490559564237419513926123520000000000000000
ii.
46663107721972076340849619428133350245357984132190810734296481947608799996614957804470731988078259143126848960413611879125592605458432000000000000000000000000
iii.
23172213523966770724123670280303621010635693971914974901987101498394969134506826670931406322436188692149594499306436597877538608022152025529531964918909222550

3.
total labeled connected graphs:
125452273648412141401139200773089339811437122262323352216462286700734387627331522885709312904647210371328794107858418293356140610389233010890575674923332327423429917033308833625087865757067009121643735335562957720919464360279849562024268481514680519466433342816295305461792608710076067024418040646132922593872156786882042514851134725907407734998659047116141535192232282791034794601497425933135733739224548153792567839779141913680549722028773475603674523853169051845195421079685934332310882053907313995168923535704556709136009686053259752740308577712484995569783650846269720521608249582420017860918845622644663874987575160515268766971368721963159046529551370104575096202684311358624098672672476994761800126366704378281769378475834662925454186722285874859694872242026068795039642380038691501013387521486053366727435218916045301026547623117868196574350026663672938544838421549439678291079144887169351257353939537143880911795509769485297854345823362270660712007071953958048732807833151699233932553517365602355625760928908188344900652899469143373311896574182769657272933821876553379518700197938172155010185719146936187180903250543579433005278984692348282568379624191843385007057047580846112172322370992146748764340302424100769640802926078370838482052406435490036434092467614465282934547622486501083341846045800849550829377015688082924233744178977266360888077466658752803757886543953371541948150838050857811138739570190403175194723845806878286855221273591078542964296886759202533689916185534005248
exactly 2 components:19792878830464097434146485069739463865673187370672887935834214122103592997909477467639145015413302778571558698199938989875722363632867076525500775193313203219625694859620492756307560817786124480904571667305985231399040766859432538780170724152051889531424530851027515639435541861971440089962657458762079240342770560135993633520904674629099681471079341302098763093130534058092714306341148454323169655736417188716167485638876856164406937663195315675056473320830072088996900023615988558834190601024551606490996047256677952803727152702099973371018028710701366236803289614033811563475696670364580819031243080945830466884602280114938472440443402744527681562033913068944126647000531086090506590597863434313244427618995892382119045374120085198882365703112462192132262796290715887651629501613500765319382697459714625232601391113377456170319146465206446792331217136689657731214890373782128820154293953635221308380687242012269185806693761170244502543846560216890121849276503785641853915478872687428718708183133628359872764435735322526121955322100244200579269171473679314961687680638065276652910066401714258899512328773662068014373263170965092624777284239415572512416129024249860116530210873861235283964287841875225918264476127609182676153172047392096718128978027994944226801334642136592881198292406724597930004937454732160477796576767954616879358825917759244042876084345101045377871469937328841023216205534951719728974096997883111102605252071058831339598818474925540591534080
exactly 100 components:
1