A281361 Number of scenarios in the Gift Exchange Game when a gift can be stolen at most 9 times.

1, 10, 352705, 3047235458767, 609542744597785306189, 1214103036523322674154687139158, 14963835327495031822418126706099787884130, 836883118002221273912672040462907783367741190535388, 170589804359366329173961838612841486616626580885839826818966688, 107640669875812795238625627484701500354901860426640161278022882392148747562, 185260259482556646382994900799988470488841686941141661692183483756531004879305895810561

Offset: 0

Author

N. J. A. Sloane, Jan 25 2017

Keywords

• nonn

Comments

More than the usual number of terms are shown in the DATA field because there are the initial values needed for one of the recurrences.

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..63
• 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.

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.

Programs

Maple

with(combinat):
b:= proc(n, i, t) option remember; `if`(t*i add(b(k, 10, n), k=0..10*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 <= 10*n := t[n, k] = Sum[(1/j!)*Product[k - m, {m, 1, j}]*t[n - 1, k - j - 1], {j, 0, 9}]; t[, ] = 0; a[n_] := Sum[t[n, k], {k, 0, 10*n}]; Table[a[n], {n, 0, 11}] (* Jean-François Alcover, Feb 18 2017 *)

PARI

{a(n) = sum(i=n, 10*n, i!*polcoef(sum(j=1, 10, x^j/j!)^n, i))/n!} \\ Seiichi Manyama, May 22 2019