A283153 Number of set partitions of unique elements from an n X 4 matrix where elements from the same row may not be in the same partition.

1, 209, 163121, 326922081, 1346634725665, 9939316337679281, 119802044788535500753, 2205421644124274191535553, 58945667435045762187763602753, 2198513228897522394476415669503377, 110833342180980170285766876408530089329, 7356710448423295420590529054176924329802529, 628972339934967292421997567343442748145219556449

Offset: 1

Author

Marko Riedel, Mar 01 2017

Keywords

• nonn

Comments

Apparently a duplicate of A071379? - 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
• Marko Riedel, Maple code for generalized Bell numbers, A000110, A020556, A069223, A283153, A283154, A283155, optimized version

Crossrefs

Cf. A283154, A283155, A071379.

Programs

Mathematica

Table[(4!^n) * Sum[Binomial[p,4]^n/p! * Sum[(-1)^k/k!,{k,0,4n-p}],{p,1,4n}],{n,1,50}] (* Indranil Ghosh, Mar 04 2017 *)

PARI

a(n) = (4!^n) * sum(p=1, 4*n, binomial(p,4)^n/p! * sum(k=0, 4*n-p, (-1)^k/k!)); \\ Indranil Ghosh, Mar 04 2017

Formula

a(n) = m!^n * Sum_{p=1..n*m} (binomial(p,m)^n/p!) * Sum_{k=0..n*m-p} (-1)^k/k! with m=4.

Extensions

If it is proved that A283153 and A071379 are the same, then the entries should be merged and A283153 recycled. - N. J. A. Sloane, Mar 06 2017