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A281358
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Number of scenarios in the Gift Exchange Game when a gift can be stolen at most 6 times.
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10
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1, 7, 6427, 216864652, 60790021361170, 79397199549271412737, 350521520018942991464535019, 4247805448772073978048752721163278, 122022975450467092259059357046375920848764, 7449370563518425038119522091529589590475534631830
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OFFSET
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0,2
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COMMENTS
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The result from the recurrence has been confirmed up to a(63) by using an optimized version of equation (23) in the Applegate-Sloane paper. - Lars Blomberg, Feb 01 2017
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LINKS
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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)
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MAPLE
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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, 7, n), k=0..7*n):
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MATHEMATICA
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t[n_, n_] = 1; t[n_ /; n >= 0, k_] /; 0 <= k <= 7*n := t[n, k] = Sum[(1/j!)*Product[k - m, {m, 1, j}]*t[n - 1, k - j - 1], {j, 0, 6}]; t[_, _] = 0; a[n_] := Sum[t[n, k], {k, 0, 7*n}]; Table[a[n], {n, 0, 10}] (* Jean-François Alcover, Feb 18 2017 *)
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PROG
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(PARI) {a(n) = sum(i=n, 7*n, i!*polcoef(sum(j=1, 7, x^j/j!)^n, i))/n!} \\ Seiichi Manyama, May 22 2019
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CROSSREFS
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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.
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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