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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. 4
1, 2, 31, 18252, 1495388159, 34155922905682979, 350521520018942991464535019, 2371013832433361706367594400829713564440, 14584126149704606223764458141727351569547933381159988406, 107640669875812795238625627484701500354901860426640161278022882392148747562 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

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

FORMULA

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

MAPLE

with(combinat):

b:= proc(n, i, t) option remember; `if`(t*i<n, 0,

      `if`(n=0, `if`(t=0, 1, 0), add(b(n-i*j, i-1, t-j)*

       multinomial(n, n-i*j, i$j)/j!, j=0..min(t, n/i))))

    end:

a:= n-> 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*i<n, 0, If[n==0, If[t==0, 1, 0], Sum[b[n-i*j, i-1, t-j]* multinomial[n, Join[{n-i*j}, Array[i&, j]]]/j!, {j, 0, Min[t, n/i]}]]]; a[n_] := Sum[b[j, n+1, n], {j, 0, (n+1)*n}]; Table[a[n], {n, 0, 10}] (* Jean-Fran├žois Alcover, Mar 13 2017, translated from Maple *)

CROSSREFS

Main diagonal of A144510, A144512.

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

Sequence in context: A004072 A113030 A247873 * A018802 A166487 A004842

Adjacent sequences:  A281898 A281899 A281900 * A281902 A281903 A281904

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Feb 01 2017

STATUS

approved

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Last modified August 21 23:00 EDT 2019. Contains 326169 sequences. (Running on oeis4.)