> #Attendence Q1:
> #What is the explicit expression for the sequence?
> #a(0)=a(1)=a(2)=0, a(n)=1 for n=3,4, ...
> #f(x):= x^3+x^4+x^5+...
> sum(x^n, n=3..infinity);
-x^3/(x-1)
> #Use maple to find an explicit expression for this generating function of 0,8,27,64,125,... a(n)=n^3
> sum(x^(3*n), n=0..infinity);
-1/(x^3-1)
> #1, n, binomial(n,2), ..., binomial(n,n) 
> #Fix n, Let a(k)= binomial(n,k)=(n+k)!/(n!*k)
> #The OGF(ordinary generating function) 1+n+binomial(n,2)*x^2+...+binomial(n,n)*x^n = (1+x)^n
> 
> #Attendence Q3:
> #Find the EGF of a(n)=n, for 0<=n<=5, a(n)=0 if n>=6
> #f(x)= x+x^2/4+x^3/6+x^4/24+x^5/120
> 
> #Attendence Q4:
> #What is the EFG of a(n)=0 for n=0,1,2,3,4,5, and a(n)=1 for n>=6
> #f(x)=x^6/6!+x^7/7!+...
> sum(x^n/n!, n=6..infinity);
exp(x)-(1/120)*x^5-(1/24)*x^4-(1/6)*x^3-(1/2)*x^2-x-1
> 
> #Attendence Q5:
> #Find the EGF of a(0)=0, a(1)=0, a(n)=(n-2)for n>=2
> sum((n-2)*x^n/n!, n=2..infinity);
(x-2)*exp(x)+x+2
> 
> #Attendence Q6:
> #What is A number of this sequence in OEIS?
> #A-1187, 	Number of connected labeled graphs with n nodes.
> #How many digit does the number of labeled connected graphs with 150 vertices? 
> [seq(i!*coeff(taylor(log(add(2^(n*(n-1)/2)*x^n/n!, n=0..150)), x=0,150),x,i), i=150)];
[57133839564458545904789328652610540031895535786011264182548375833179829124845398393126574488675311145377107878746854204162666250198684504466355949195922066574942592095735778929325357290444962472405416790722118445437122269675520000000000000000000000000000000000000*O(1)]
> 
> #Attendence Q7:
> #Use the technique of weight enumeration to find the exact number of sequences a[1],a[2],...,a[r], (r can be any length)
> #where each of the a[i] is a member of {3,4,7} that add-up to 1001 
> f:=1/(1-x^3-x^4-x^7);
f := 1/(-x^7-x^4-x^3+1)
> coeff(taylor(f,x=0, 1002), x, 1001);
37327228629056835260060479719213438237141848693395064396004356099234232222305300761357555310103620202925186169
> 
> #Attendence Q8:
> #Is [{{1,3,4},{6,7}}, 52] a member of X(7)?
> #No
> #why yet?
> #The first part should be length of permutation which is not a SP
> #How big is X(100)?
> #edf(X) = egf(PERMUTATION)*egf(SETPARTITIONS)
> f:=1/(1-x)*exp(exp(x)-1);
f := exp(exp(x)-1)/(1-x)
> coeff(taylor(f,x=0, 101), x,100)*100!;
520288193827224460161665693343439067946826765691270139531070491212113377307944087322830833805396364699434666974424650987403343482352896062075174445266247411051
> 
> #Attendence Q9:
> #later on we will prove that the egf of labelled trees is 
> #Sum(n^(n-2)*x^n/n!, n=1..infinity)
> #
> #How many triples of the form  [Labeled Tree, Permutation, SetPartion]
> #of size 150 (meaning that the number of vertices of the tree + the length of the permuttaion + the size of the set that set partitions is exactly 150)
> #
> coeff(taylor(sum(n^(n-2)*x^n/n!, n=1..infinity)+1/(1-x)+exp(exp(x)-1), x=0, 151), x, 150);
11521428797724199759754908747468811327256490048728103905960023234706648015084044740821532520269056707733020791253437837258812876479375734650856218219059122703948737669867959080915946719728024356376766778599247259089817422525283274851147747866305132222433091707072845267088845997860081807698260131483895128968898878663077403/57133839564458545904789328652610540031895535786011264182548375833179829124845398393126574488675311145377107878746854204162666250198684504466355949195922066574942592095735778929325357290444962472405416790722118445437122269675520000000000000000000000000000000000000
>