#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:

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

Q1. 
	When does Rabbi Levi Ben Gerson born? 

A1. 
	1288

Q2. 
	When was Bell number creator born? When was he died? What is he famous for? 
A2. 
	Died 1960. Born 1883. Famous for Bell series, polynomials, triangles etc. 

Q3. 
	What is the pen name for E.T. bell? 
A3. 
	John Taine

Q4. 
	How many set partitions of a 300-lement set are there with exactly 5 members? 
A4. 
		Snk(300, 5) = 4090911221081438794246476628982333220442638220478190976605825883041810075846210707549539683575840119419320444839733557924380958558669263052623178486192842007420476226080784639399165079562132928175942227395000

Q5.
	Is this sequence in the OEIS? [57:19]
	1, 1, 4, 11, 41, 162, 715

A5. 
	A000296 set partitions without singletons 

Q6. 
	Is this in the OEIS? 
	1, 1, 4, 10, 40, 140, 630, 2800
A6.
	No. 

Q7. 
	Let a_k(n): be the number of permutations where every cycle is of length at least k, 

	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?

A7. 
	For k = 3,  [in OEIS]
	0, 0, 6, 24, 120, 720, 6300, 58464, 586656, 6384960, 76471560, 994831200, 13939507296, 209097854784, 3345235180560, 56866395720960, 1023601917024000, 19448577603454464, 388972171805410656, 8168409582839579520, 179704944537482689920, 4133213636880538425600, 99197131945856677419456, 2479928332674564111757824, 64478136551481363914841600, 1740909683073851861225241600, 48745471108643784941792976000, 1413618662349077210550915116544, 42408559873877916528445525618176

	k = 4, [in OEIS]
	0, 0, 0, 24, 120, 720, 5040, 40320, 435456, 4959360, 60255360, 782939520, 10870104960, 162642864384, 2602111599360, 44265739714560, 797239080529920, 15148603957800960, 302953165014675456, 6361636837067089920, 139952704431008286720, 3218922790460015063040, 77254605493692206469120, 1931370859803315548749824, 50215664438816457218457600, 1355822305759073660955033600, 37963012534836747190338355200, 1100927264115029271588399513600, 33027818402324374018424155570176

	k = 5, [not in OEIS]
	0, 0, 0, 0, 120, 720, 5040, 40320, 362880, 3628800, 46569600, 627264000, 8932809600, 134745811200, 2151954604800, 36333345484800, 652247595417600, 12385384471756800, 247786790166835200, 5206427690158080000, 114589796403688704000, 2635791799280758272000, 63256908904042258944000, 1581337219487520337920000, 41113219946575682949120000, 1110041176225999576965120000, 31081211869742363266928640000, 901359406516783722230661120000, 27040871695014672559996538880000