> #Attendence Q1.
> #When was Rabbi Levi Ben Gerson born and died?
> #He was born in 1288 and died in 1344
> 
> #Attendence Q2.
> #When was E. T. Bell born and died? What is his famous for? What is the name of his famous book about the history of mathematics?
> #He was born in 1883 and died in 1960. "Men of Mathematics".
> 
> #Attendence Q3.
> #What is the pen name of Bell?
> #His pen name is John Taine.
> 
> read `M20.txt`;
> Help20();
` SnkSeq(N,k), SnkSeqC(N,k), ReducedCycle(C), PtoCfull(C),  cnk(n,k) , cnkSeq(N,k), cnkSeqC(N,k) `
> #Attendence Q4.
> #How many set partition of 300 element set are there with exacxtly 5 members?
> Snk(300,5);
4090911221081438794246476628982333220442638220478190976605825883041810075846210707549539683575840119419320444839733557924380958558669263052623178486192842007420476226080784639399165079562132928175942227395000
> 
> #Attendence Q5.
> #Is this sequence in OEIS? If it is, what is A number? 
> #Yes. A296
> 
> #Attendence Q6.
> #Is this sequence in OEIS? If it is, what is A number? 
> #No. This one is not in OEIS.
> 
> #Attendence Q7
> #Let a_k(n): be the number of permutations where every cycle is of length at least k.
> #a_1(n)=n! a_2(n)=d(n)
> #for k=3,4,5, find the first 30 terms of a_k(n) and see whether there are already in the OEIS? Which k  is the smallest that is not there? Should it be?
> #
> #for k = 3, 
> f3:= taylor(exp(-log(1-x)-x-x^2/2!), x=0, 31):
> [seq(i!*coeff(f3,x,i), i=1..30)];
[0, 0, 2, 6, 24, 160, 1140, 8988, 80864, 809856, 8907480, 106877320, 1389428832, 19452141696, 291781655984, 4668504894480, 79364592318720, 1428562679845888, 27142690734936864, 542853814536802656, 11399930109077490560, 250798462399300784640, 5768364635100620089152, 138440751242507472273856, 3461018781064593367693824, 89986488307675206245836800, 2429635184307185219369763200, 68029785160601345467104670848, 1972863769657440129000783404544, 59185913089723198139150966450176]
> #for k =4,
> f4:=taylor(exp(-log(1-x)-x-x^2/2!-x^3/3!), x=0, 31):
> [seq(i!*coeff(f4,x,i), i=1..30)];
[0, 0, 1, 6, 24, 130, 930, 7644, 68824, 685656, 7535340, 90457840, 1176171216, 16466275176, 246988107184, 3951794537040, 67180633256640, 1209252349298944, 22975793737934544, 459515836026817056, 9649832432640849280, 212296314644126875680, 4882815247362243598176, 117187565931600216644416, 2929689147731179453981824, 76171917838532634871190400, 2056641781659044077126158400, 57585969886697625971808647424, 1669993126714400894865685465344, 50099793801417192589876087970176]
> #for k =5,
> f5:=taylor(exp(-log(1-x)-x-x^2/2!-x^3/3!-x^4/4!), x=0, 31):
> [seq(i!*coeff(f5,x,i), i=1..30)];
[0, 0, 1, 5, 24, 130, 895, 7259, 65800, 658356, 7234215, 86772235, 1128043136, 15793597170, 236909199709, 3790544072665, 64439047006160, 1159901713071064, 22038133521682785, 440762728595139381, 9256017668688582280, 203632388424110113370, 4683544911007142001591, 112405077697364465285635, 2810126942480860743464824, 73063300516110209971967900, 1972709114035507833676795975, 55235855193051777120662297499, 1601839800591088168046023229520, 48055194017655158162354726374426]
> #sequence of f3 is in the OEIS, A038205
> #sequence of f4 and f5 are not in the OEIS.
> #The smallest k that is not in the OEIS is 4.
> 
> 
>