A281901 Number of scenarios in the Gift Exchange Game with n players and n wrapped gifts when a gift can be stolen at most n times.

1, 2, 31, 18252, 1495388159, 34155922905682979, 350521520018942991464535019, 2371013832433361706367594400829713564440, 14584126149704606223764458141727351569547933381159988406, 107640669875812795238625627484701500354901860426640161278022882392148747562

Offset: 0

Author

Alois P. Heinz, Feb 01 2017

Keywords

• nonn

Comments

Also total number of partitions of [k] into exactly n nonempty blocks, each of size at most n+1, for any k in the range n <= k <= n^2+n.

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..26
• Moa Apagodu, David Applegate, N. J. A. Sloane, and Doron Zeilberger, Analysis of the Gift Exchange Problem, arXiv:1701.08394, 2017.
• Moa Apagodu, David Applegate, N. J. A. Sloane, and Doron Zeilberger, On-Line Appendix I to "Analysis of the gift exchange problem"
• Moa Apagodu, David Applegate, N. J. A. Sloane, and Doron Zeilberger, On-Line Appendix II to "Analysis of the gift exchange problem"
• David Applegate and N. J. A. Sloane, The Gift Exchange Problem, arXiv:0907.0513 [math.CO], 2009.

Crossrefs

Main diagonal of A144510, A144512.

Cf. A001515, A144416, A144508, A144509, A149187, A281358, A281359, A281360, A281361.

Programs

Maple

with(combinat):
b:= proc(n, i, t) option remember; `if`(t*i add(b(j, n+1, n), j=0..(n+1)*n):
seq(a(n), n=0..10);

Mathematica

multinomial[n_, k_List] := n!/Times @@ (k!); b[n_, i_, t_] := b[n, i, t] = If[t*iJean-François Alcover, Mar 13 2017, translated from Maple *)

Formula

a(n) = A144510(n+1,n) = A144512(n,n).