A283154 Number of set partitions of unique elements from an n X 5 matrix where elements from the same row may not be in the same partition.

1, 1546, 12962661, 363303011071, 25571928251231076, 3789505947767235111051, 1049433111253356296672432821, 498382374325731085522315594481036, 380385281554629647028734545622539438171, 443499171330317702437047276255605780991365151, 758311423589226886694849718263394302618332719358226

Offset

1,2

Comments

Apparently a duplicate of A090209. - R. J. Mathar, Mar 06 2017

Links

Indranil Ghosh, Table of n, a(n) for n = 1..50

M. Riedel, Set partitions of unique elements from an n-by-m matrix where elements from the same row may not be in the same partition

Formula

a(n) = m!^n Sum_{p=1..n*m} (Choose(p,m)^n/p!) Sum_{k=0..n*m-p} (-1)^k/k! with m=5.

Mathematica

Table[(5 !^n)*Sum[Binomial[p, 5]^n/p ! * Sum[(-1)^k/k !, {k, 0, 5n-p}], {p, 1, 5n}], {n, 1, 11}] (* Indranil Ghosh, Mar 04 2017 *)

Prog

(PARI) a(n) = (5!^n)*sum(p=1, 5*n, binomial(p, 5)^n/p! * sum(k=0, 5*n-p, (-1)^k/k!)); \\ Indranil Ghosh, Mar 04 2017

Crossrefs

Cf. A283153, A283155.

Sequence in context: A249473 A246899 A090209 * A157347 A255356 A336221

Adjacent sequences: A283151 A283152 A283153 * A283155 A283156 A283157

Keyword

nonn

Author

Marko Riedel, Mar 01 2017

Extensions

If it is proved that A283154 and A090209 are the same, then the entries should be merged and A283154 recycled. - N. J. A. Sloane, Mar 06 2017

Status

approved