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A281361
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Number of scenarios in the Gift Exchange Game when a gift can be stolen at most 9 times.
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10
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1, 10, 352705, 3047235458767, 609542744597785306189, 1214103036523322674154687139158, 14963835327495031822418126706099787884130, 836883118002221273912672040462907783367741190535388, 170589804359366329173961838612841486616626580885839826818966688, 107640669875812795238625627484701500354901860426640161278022882392148747562, 185260259482556646382994900799988470488841686941141661692183483756531004879305895810561
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OFFSET
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0,2
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COMMENTS
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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.
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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, 10, n), k=0..10*n):
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MATHEMATICA
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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 *)
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PROG
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(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
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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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STATUS
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approved
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