#ATTENDANCE QUIZ FOR LECTURE 20 of Dr. Z.'s Math454(02) Rutgers University

# Please Edit this .txt page with Answers

#Email  ShaloshBEkhad@gmail.com 
#Subject: p20
#with an attachment called
#p20FirstLast.txt
#(e.g. p19DoronZeilberger.txt)

#Right after finishing watching the lecture but no later than Nov. 17, 2020, 8:00pm


THE NUMBER OF ATTENDANCE QUESTIONS WERE: 5

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

1. When was Rabbi Levi Ben Gerson born and when did he die?
born 1288 and died 1344

2. How many set partitions of a 300-element set are there with exactly 5 members?
Snk(300,5)= 4090911221081438794246476628982333220442638220478190976605825883041810075846210707549539683575840119419320444839733557924380958558669263052623178486192842007420476226080784639399165079562132928175942227395000

3. Is 1,1,4,11,41,162,715,3425,17722,98253,580317,3633280,24011157 in the OEIS? What is the A-number?
yes, A000296

4. 0,1,1,4,10,40,140,630,2800,14070,73150,412720,2422420,..
Is it in the OEIS? A number?
no

5. 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,k=4,k=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?

cnkSeq(20, 3) =
[0, 0, 1, 6, 35, 225, 1624, 13132, 118124, 1172700, 12753576, 150917976, 1931559552, 26596717056, 392156797824, 6165817614720, 102992244837120, 1821602444624640, 34012249593822720, 668609730341153280]
A081051

cnkSeq(20, 4) = 
[0, 0, 0, 1, 10, 85, 735, 6769, 67284, 723680, 8409500, 105258076, 1414014888, 20313753096, 310989260400, 5056995703824, 87077748875904, 1583313975727488, 30321254007719424, 610116075740491776]
no


cnkSeq(20, 5) = 
[0, 0, 0, 0, 1, 15, 175, 1960, 22449, 269325, 3416930, 45995730, 657206836, 9957703756, 159721605680, 2706813345600, 48366009233424, 909299905844112, 17950712280921504, 371384787345228000]
no

k=3 is the smallest
no