OFFSET
0,2
COMMENTS
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.
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..69
Moa Apagodu, David Applegate, N. J. A. Sloane, and Doron Zeilberger, Analysis of the Gift Exchange Problem, arXiv:1701.08394 [math.CO], 2017.
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)
David Applegate and N. J. A. Sloane, The Gift Exchange Problem, arXiv:0907.0513 [math.CO], 2009.
MAPLE
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, 9, n), k=0..9*n):
seq(a(n), n=0..12); # Alois P. Heinz, Feb 01 2017
MATHEMATICA
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 *)
PROG
(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
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Jan 25 2017
STATUS
approved