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

Author

Marko Riedel, Mar 01 2017

Keywords

• nonn

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

Crossrefs

Cf. A283153, A283155.

Programs

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 *)

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

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.

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