A281359 Number of scenarios in the Gift Exchange Game when a gift can be stolen at most 7 times.

1, 8, 24301, 5165454442, 12845435390707724, 191739533381111401455478, 11834912423104188943497126664597, 2371013832433361706367594400829713564440, 1299618941291522676629215597535104557826094801396, 1716119248126070756229849154290399886241087778087554633612

Offset

0,2

Links

Seiichi Manyama, Table of n, a(n) for n = 0..77

Moa Apagodu, David Applegate, N. J. A. Sloane, and Doron Zeilberger, Analysis of the Gift Exchange Problem, arXiv:1701.08394 [math.CO], 2017.

Moa Apagodu, David Applegate, N. J. A. Sloane, and Doron Zeilberger, On-Line Appendix I to "Analysis of the gift exchange problem", giving Type D recurrences for G_1(n) through G_15(n) (see A001515, A144416, A144508, A144509, A149187, A281358-A281361)

Moa Apagodu, David Applegate, N. J. A. Sloane, and Doron Zeilberger, On-Line Appendix II to "Analysis of the gift exchange problem", giving Type C recurrences for G_1(n) through G_15(n) (see A001515, A144416, A144508, A144509, A149187, A281358-A281361)

David Applegate and N. J. A. Sloane, The Gift Exchange Problem, arXiv:0907.0513 [math.CO], 2009.

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(k, 8, n), k=0..8*n):
seq(a(n), n=0..12);  # Alois P. Heinz, Feb 01 2017

Mathematica

t[n_, n_] = 1; t[n_ /; n >= 0, k_] /; 0 <= k <= 8*n := t[n, k] = Sum[(1/j!)*Product[k - m, {m, 1, j}]*t[n - 1, k - j - 1], {j, 0, 7}]; t[_, _] = 0; a[n_] := Sum[t[n, k], {k, 0, 8*n}]; Table[a[n], {n, 0, 10}] (* Jean-François Alcover, Feb 18 2017 *)

Prog

(PARI) {a(n) = sum(i=n, 8*n, i!*polcoef(sum(j=1, 8, x^j/j!)^n, i))/n!} \\ Seiichi Manyama, May 22 2019

Crossrefs

The gift scenarios sequences when a gift can be stolen at most s times, for s = 1..9, are A001515, A144416, A144508, A144509, A149187, A281358, A281359, A281360, A281361.

Sequence in context: A173543 A067074 A220942 * A067070 A115478 A221629

Adjacent sequences: A281356 A281357 A281358 * A281360 A281361 A281362

Keyword

nonn

Author

N. J. A. Sloane, Jan 25 2017

Status

approved