cp's OEIS Frontend

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

%I A281361 #31 May 22 2019 14:16:55
%S A281361 1,10,352705,3047235458767,609542744597785306189,
%T A281361 1214103036523322674154687139158,
%U A281361 14963835327495031822418126706099787884130,836883118002221273912672040462907783367741190535388,170589804359366329173961838612841486616626580885839826818966688,107640669875812795238625627484701500354901860426640161278022882392148747562,185260259482556646382994900799988470488841686941141661692183483756531004879305895810561
%N A281361 Number of scenarios in the Gift Exchange Game when a gift can be stolen at most 9 times.
%C A281361 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.
%H A281361 Seiichi Manyama, <a href="/A281361/b281361.txt">Table of n, a(n) for n = 0..63</a>
%H A281361 Moa Apagodu, David Applegate, N. J. A. Sloane, and Doron Zeilberger, <a href="http://arxiv.org/abs/1701.08394">Analysis of the Gift Exchange Problem</a>, arXiv:1701.08394 [math.CO], 2017.
%H A281361 Moa Apagodu, David Applegate, N. J. A. Sloane, and Doron Zeilberger, <a href="/A144416/a144416.txt">On-Line Appendix I to "Analysis of the gift exchange problem"</a>, giving Type D recurrences for G_1(n) through G_15(n) (see A001515, A144416, A144508, A144509, A149187, A281358-A281361)
%H A281361 Moa Apagodu, David Applegate, N. J. A. Sloane, and Doron Zeilberger, <a href="/A144416/a144416_1.txt">On-Line Appendix II to "Analysis of the gift exchange problem"</a>, giving Type C recurrences for G_1(n) through G_15(n) (see A001515, A144416, A144508, A144509, A149187, A281358-A281361)
%H A281361 David Applegate and N. J. A. Sloane, <a href="http://arxiv.org/abs/0907.0513">The Gift Exchange Problem</a>, arXiv:0907.0513 [math.CO], 2009.
%p A281361 with(combinat):
%p A281361 b:= proc(n, i, t) option remember; `if`(t*i<n, 0,
%p A281361       `if`(n=0, `if`(t=0, 1, 0), add(b(n-i*j, i-1, t-j)*
%p A281361        multinomial(n, n-i*j, i$j)/j!, j=0..min(t, n/i))))
%p A281361     end:
%p A281361 a:= n-> add(b(k, 10, n), k=0..10*n):
%p A281361 seq(a(n), n=0..12);  # _Alois P. Heinz_, Feb 01 2017
%t A281361 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 *)
%o A281361 (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
%Y A281361 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.
%K A281361 nonn
%O A281361 0,2
%A A281361 _N. J. A. Sloane_, Jan 25 2017