#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:7

PLEASE LIST ALL THE QUESTIONS FOLLOWED, AFTER EACH, BY THE ANSWER
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1. When was Rabbi Levi Ben Gerson born? When did he die?
A1. Rabi Levi Ben Gerson was born in 1288 and died on April 20 1344.

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2. When was E.T.Bell born and when did he die? What was he famous for?
A2. He was born on February 7th 1883 in Peterhead (UK) and died in Dec 21 1960 in Watsonville (CA).
	He was a famour mathematician who's known work include 	Number theory, Bell numbers and 
	his books Men of Mathematics and The development of Mathematics.
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3. What was ET Bell's pen name?
A3. His pen name was John Taine. 

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4. How many set-partitions of 300 elements are there with exactly 5 members?
A4. Snk(300, 5);
4090911221081438794246476628982333220442638220478190976605825883\

  04181007584621070754953968357584011941932044483973355792438095\

  85586692630526231784861928420074204762260807846393991650795621\

  32928175942227395000

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5. Is 1,1,4,11,41,162,715,3425,17722,98253,580317,3633280,24011157 on OEIS? A-number?
A5. Yes. A-number:= A000296

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6. Is 0, 1, 1, 4, 10, 40, 140, 630, 2800, 14070, 73150, 412720, 2422420, 15095080, 98098000 on OEIS?
A6. No. 

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7. 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 they are in OEIS. Which k
is the smallest that is not there? Should it be?
A7. a_t := proc(n, k) local l, i; l := []; i := k; while 0 < i do l := [op(l), cnk(n, i)]; i := i - 1; end do; l; end proc;
a_t(35, 30);
[413836815700, 33269993069280, 2189048024902200, 

  120136985818233846, 5576855646887454930, 221290735245426237300, 

  7566115331692217391000, 224264025782510898227340, 

  5789007068900388322350900, 130570338239752489337859600, 

  2579028773194868843780085000, 44668807034505239122701256785, 

  678699133190453314288471012275, 

  9042798594534503414149286022050, 

  105523885793994336407478050234000, 

  1076269687422110767154005483983104, 

  9565726401492592499535375980360480, 

  73791435901813055443997302183340480, 

  491524576355157382522963214293356800, 

  2808648075987685663731827003710271232, 

  13654954590729087538995349554393465600, 

  55901429045378401775473854399630021120, 

  190184293406442993287964540251118796800, 

  528639086316507052387657081720980455424, 

  1173832006833713383837776254766133739520, 

  2018934961056924073346381828162273280000, 

  2572570869342194059028609542178734080000, 

  2264982182865483679253566222746255360000, 

  1215830662512066538628209615621324800000, 

  295232799039604140847618609643520000000]

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