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

%I A281359 #30 May 22 2019 21:03:48
%S A281359 1,8,24301,5165454442,12845435390707724,191739533381111401455478,
%T A281359 11834912423104188943497126664597,
%U A281359 2371013832433361706367594400829713564440,1299618941291522676629215597535104557826094801396,1716119248126070756229849154290399886241087778087554633612
%N A281359 Number of scenarios in the Gift Exchange Game when a gift can be stolen at most 7 times.
%H A281359 Seiichi Manyama, <a href="/A281359/b281359.txt">Table of n, a(n) for n = 0..77</a>
%H A281359 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 A281359 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 A281359 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 A281359 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 A281359 with(combinat):
%p A281359 b:= proc(n, i, t) option remember; `if`(t*i<n, 0,
%p A281359       `if`(n=0, `if`(t=0, 1, 0), add(b(n-i*j, i-1, t-j)*
%p A281359        multinomial(n, n-i*j, i$j)/j!, j=0..min(t, n/i))))
%p A281359     end:
%p A281359 a:= n-> add(b(k, 8, n), k=0..8*n):
%p A281359 seq(a(n), n=0..12);  # _Alois P. Heinz_, Feb 01 2017
%t A281359 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 *)
%o A281359 (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
%Y A281359 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 A281359 nonn
%O A281359 0,2
%A A281359 _N. J. A. Sloane_, Jan 25 2017