#ATTENDANCE QUIZ FOR LECTURE 19 of Dr. Z.'s Math454(02) Rutgers University

# Please Edit this .txt page with Answers

#Email  ShaloshBEkhad@gmail.com 
#Subject: p19
#with an attachment called
#p19FirstLast.txt
#(e.g. p19DoronZeilberger.txt)

#Right after finishing watching the lecture but no later than Nov. 13, 2020, 8:00pm


THE NUMBER OF ATTENDANCE QUESTIONS WERE: 8

PLEASE LIST ALL THE QUESTIONS FOLLOWED, AFTER EACH, BY THE ANSWER

Question 1
i)WHat is the explicitly expression for the sequence a(0) a(1) = 0, a(2) = 0 a(3) = 1 ...
ii) Use maple to find an explicit expression for the generating function a(n) = n^3
iii) Basically the binomial theorem

Answer 1
i) -x^3/(-1 + x)
ii) x*(x^2 + 4*x + 1)/(-1 + x)^4
iii) (1 + x)^n

Question 2
Find the egf of a(n) = n for 0<=n<=5, a(n) if n>=6

Answer 2
x + x^2 + 1/2*x^3 + 1/6*x^4 + 1/24*x^5

Question 3
Whatis the EGF of a(n) for n =0,1,2,3,4,5 and a(n) = 1 for n>=6

Answer 3
exp(x) - x^5/120 - x^4/24 - x^3/6 - x^2/2 - x - 1

Question 4
Find the egf of a(0) = 0 a(n) = n-2! for n>=2

Answer 4
-x*ln(1 - x) + ln(1 - x) + x

Question 5
i) What is the OEIS A number of this question
ii) How many digits does the number of labeled connected graphs with 150 vertices has 
Answer 5
i) A001187
ii) 3365

Question 6
Use the technique of weight enumeration to find the exact number of sequences a[1], a[2], a[3], a[4] ... 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

Question 6
37327228629056835260060479719213438237141848693395064396004356099234232222305300761357555310103620202925186169

Question 7
Is [{{1, 3, 4}, {6, 7}}, 52] a member of X(7)\

Answer 7
Yes it is since 3+2+2 = 7

Question 8

How many triples of the form [labeled tree, permutation, set partition]

Answer 8