> #Attendance Quiz 19
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> 
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> #THE NUMBER OF ATTENDANCE QUESTIONS WERE: 8
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> 
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> #Q1
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> #What is the explicit expression for the sequence a(0) = 0, a(1) = 0, a(2) = 0, a(n) = 1 for n = 3, 4... 
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> #Use Maple to find an explicit expression for the generating function of 0,1,8,27,64,125, ... a(n) = n^3
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> 
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> 
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> #f(x)=0+0+0+x^3+x^4+x^5+...      => f(x) = x^3/(1-x) 
> #sum(x^n*n^3, n = 0 .. infinity) => x*(x^2 + 4*x + 1)/(x - 1)^4
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> 
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> 
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> #Q2
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> #Find the EGF of a(n)=n, for 0<=n<=5, a(n)=0 if n>=6
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> 
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> #a(0)x/0!+a(1)x/1!+a(2)x/2!+a(3)x/3!+a(4)x/4!+a(5)x/5

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> #Q3
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> #What is the EFS of a(n) =0 for n=0,1,2,3,4,5 and a(n)=1 for n>=6
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> 
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> #x^6/6! + x^7/7! + x^8/8! + .... = Sum(x^n/n!, n = 6..infinity) 
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> 
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> #Q4
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> #Find the EGF of a(0) = 0, a(1) = 0, a(n) = (n-2)! for n >= 2
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> 
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> #Sum(x^n/(n*(n-1)), n = 0 .. infinity) 
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> 
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> #Q5
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> #What is the A-Number of this sequence ([1,1,4,38,728, 26704....])?
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> #How many digits does the number of labeled graphs with 150 vertices have?
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> 
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> #A001187
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> 
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> #Q6
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> #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.
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> 
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> f:=1/(1-x^3-x^4-x^7)
f := 1/(-x^7-x^4-x^3+1)
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> coeff(taylor(f,x=0, 1002), x, 1001)
37327228629056835260060479719213438237141848693395064396004356099234232222305300761357555310103620202925186169
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> 
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> #Q7
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> #Is [{{1,3,4},{6,7}}, 52] a member of X(7)? Why? 
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> 
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> #No
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> 
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> #Q8
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> #Later on we will prove that the egf of labelled trees is 1+Sum(n^(n-2)*x^n/n!, n=1..infinity) How many triples of the form [Labeled Tree, Permutation, SetPartition] of size 150 (meaning num of vertices of the tree + length of permutation + size of set that SetPartition partitions is 150)?
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> 
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> #coeff(taylor(exp(exp(x) - 1)/(1 - x) + sum(n^(n - 2)*x^n/n!, n = 1 .. infinity), x = 0, 151), x, 150)*150!
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> #11521428797724199759754908747468811327256490048728103905960023234706648015084044740821532520269056707733020791253437837258812876479375734650856218219059122703948737669867959080915946719728024356376766778599247259089817422525283274851147747866305132222433091707072845267088845997860081807698260131483895128968898878663077403/57133839564458545904789328652610540031895535786011264182548375833179829124845398393126574488675311145377107878746854204162666250198684504466355949195922066574942592095735778929325357290444962472405416790722118445437122269675520000000000000000000000000000000000000
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