#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


1. When was Rabbi Levi Ben Gerson born?
A: 1288-1344


2. How many set partitions of a 300-element set are there with exactly 5 members? 
A: SPk(300,5) 


3. Is 1, 1, 4, 11, 41, 162, 715, 3425, 17722, 98253, 580317, 3633280, 24011157 in the OEIS? 
A: Yes - A000296


4. Is it in the OEIS? 
A: No 


5. Let a_k(n): Be the number of permutations where every cycle of its 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 already in the OEIS? Which k is the smallest that is not there? 
A: 


cnkSeq(30, 3);
[0, 0, 1, 6, 35, 225, 1624, 13132, 118124, 1172700, 12753576, 


  150917976, 1931559552, 26596717056, 392156797824, 


  6165817614720, 102992244837120, 1821602444624640, 


  34012249593822720, 668609730341153280, 13803759753640704000, 


  298631902863216384000, 6756146673770930688000, 


  159539850276066860544000, 3925495373278097719296000, 


  100480171548351161548800000, 2671674589068831403868160000, 


  73689668464006010184007680000, 2105684281550279072336117760000, 


  62262192842035613491057459200000]


This is in OEIS - A081051




cnkSeq(30, 4);
[0, 0, 0, 1, 10, 85, 735, 6769, 67284, 723680, 8409500, 


  105258076, 1414014888, 20313753096, 310989260400, 


  5056995703824, 87077748875904, 1583313975727488, 


  30321254007719424, 610116075740491776, 12870931245150988800, 


  284093315901811468800, 6548684852703068697600, 


  157375898285941510732800, 3936561409138663118131200, 


  102339530601744675672576000, 2761307967193712729035776000, 


  77226989703299075087834112000, 2236045380156380112643362816000, 


  66951000306085302338993639424000]


Not in OEIS


cnkSeq(30, 5);
[0, 0, 0, 0, 1, 15, 175, 1960, 22449, 269325, 3416930, 45995730, 


  657206836, 9957703756, 159721605680, 2706813345600, 


  48366009233424, 909299905844112, 17950712280921504, 


  371384787345228000, 8037811822645051776, 181664979520697076096, 


  4280722865357147142912, 105005310755917452984576, 


  2677503356427960382362624, 70874145319837672677196800, 


  1945067308917524165279692800, 55278125307966865191587481600, 


  1625014498326371300452283596800, 


  49361465831621147825759587123200]




Not in OEIS