A144509 a(n) = total number of partitions of [1, 2, ..., k] into exactly n blocks, each of size 1, 2, ..., 5, for 0 <= k <= 5n.

1, 5, 456, 405408, 1495388159, 15467641899285, 361207016885536095, 16557834064546698285496, 1350410785161120363519024709, 182141025850694258874753732988078, 38395944834298393218465758049745918098, 12093097322244029427838390643054170162054258, 5485321312184901565806045962453632525844948020084

Offset: 0

Author

David Applegate and N. J. A. Sloane, Dec 15 2008

Keywords

• nonn

Comments

Also, number of scenarios in the Gift Exchange Game when a gift can be stolen at most 4 times. - N. J. A. Sloane, Jan 25 2017

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..100
• 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.

Crossrefs

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.

Programs

Mathematica

t[n_, n_] = 1; t[n_ /; n >= 0, k_] /; 0 <= k <= 5*n := t[n, k] = Sum[(1/j!)*Product[k - m, {m, 1, j}]*t[n - 1, k - j - 1], {j, 0, 4}]; t[, ] = 0; a[n_] := Sum[t[n, k], {k, 0, 5*n}]; Table[a[n], {n, 0, 15}] (* Jean-François Alcover, Feb 18 2017 *)

PARI

{a(n) = sum(i=n, 5*n, i!*polcoef(sum(j=1, 5, x^j/j!)^n, i))/n!} \\ Seiichi Manyama, May 22 2019