#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:

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




#ATTENDANCE Q. #1 for LECTURE 19
#What is the explicit expression for the sequence a(0)=0,a(1)=0,a(2)=0,a(n)=1 for n=3,4...
#Use maple to find an explicit expression for the generating function of 0,1,8,27,64,125 a(n)=n^3

#ANSWER to Q. #1:	

# i) -x^3/(x-1)
# ii) x*(x^2+4*x+1)/(x-1)^4



#ATTENDANCE Q. #2 for LECTURE 19
#EGF for n=0,1,2,3,4,5?

#ANSWER to Q. #2:

# f(x) = x*e^x




#ATTENDANCE Q. #3 for LECTURE 19
#EGF of a(0)=0,a(1)=0,a(n)=(n-2)! for n >= 2

#ANSWER to Q. #3:

# x*ln(-x+1)+ln(-x+1)+x




#ATTENDANCE Q. #4 for LECTURE 19
#A number of the sequence? How many digits does the number of labeled connected graphs with 150 vertices have?

#ANSWER to Q. #4:

#add(coeff((s^3+s^4+s^7)^i,s,1001),i=0..335) = 37327228629056835260060479719213438237141848693395064396004356099234232222305300761357555310103620202925186169




#ATTENDANCE Q. #5 for LECTURE 19
#is [{{1,2,4},{6,7}] a member of X(7)?

#ANSWER to Q. #5:

Yes, length(pi) would be 2 (perm of 3,5), and 2 + 5 (length of set SP is partitioning) = 7 = n




#ATTENDANCE Q. #6 for LECTURE 19
# How many triples of the form Labled Tree, Permutaion, SetPartition of size 150 ?

#ANSWER to Q. #6:

#I wanted to obtain the egf in f(x) form from sum((n)^(n-2)*x^n/n!,n=1..infinity), but the sum diverges
# so I am not sure how to multiply that egf by our previous two egf's to put it into the taylor
# expression coeff(taylor(egf * exp(exp(x)-1)/(1-x),x=0,151),x,150)*150!