This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A281360 #30 May 22 2019 21:03:41
%S A281360 1,9,92368,124762262630,2774049143394729653,
%T A281360 476872353039366288373555323,414678423576860263798348331987688320,
%U A281360 1383884737648788823775562903922773021277571568,14584126149704606223764458141727351569547933381159988406,419715170056359079715862408734598208208707081189266290220651371206
%N A281360 Number of scenarios in the Gift Exchange Game when a gift can be stolen at most 8 times.
%C A281360 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 A281360 Seiichi Manyama, <a href="/A281360/b281360.txt">Table of n, a(n) for n = 0..69</a>
%H A281360 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 A281360 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 A281360 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 A281360 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 A281360 with(combinat):
%p A281360 b:= proc(n, i, t) option remember; `if`(t*i<n, 0,
%p A281360 `if`(n=0, `if`(t=0, 1, 0), add(b(n-i*j, i-1, t-j)*
%p A281360 multinomial(n, n-i*j, i$j)/j!, j=0..min(t, n/i))))
%p A281360 end:
%p A281360 a:= n-> add(b(k, 9, n), k=0..9*n):
%p A281360 seq(a(n), n=0..12); # _Alois P. Heinz_, Feb 01 2017
%t A281360 t[n_, n_] = 1; t[n_ /; n >= 0, k_] /; 0 <= k <= 9*n := t[n, k] = Sum[(1/j!)*Product[k - m, {m, 1, j}]*t[n - 1, k - j - 1], {j, 0, 8}]; t[_, _] = 0; a[n_] := Sum[t[n, k], {k, 0, 9*n}]; Table[a[n], {n, 0, 10}] (* _Jean-François Alcover_, Feb 18 2017 *)
%o A281360 (PARI) {a(n) = sum(i=n, 9*n, i!*polcoef(sum(j=1, 9, x^j/j!)^n, i))/n!} \\ _Seiichi Manyama_, May 22 2019
%Y A281360 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 A281360 nonn
%O A281360 0,2
%A A281360 _N. J. A. Sloane_, Jan 25 2017