A283155 Number of set partitions of unique elements from an n X 6 matrix where elements from the same row may not be in the same partition.

1, 13327, 1395857215, 637056434385865, 893591647147188285577, 3104750712141723393459934903, 23094793819000630529788087185212647, 331114050237261411471736187067402011971825, 8452444659410086110360476363825233533247222327537, 361084373753302872550305348321621374196786909194880037375

Offset: 1

Author

Marko Riedel, Mar 01 2017

Keywords

• nonn

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, A283154.

Programs

Mathematica

Table[(6!^n)*Sum[Binomial[p,6]^n/p! * Sum[(-1)^k/k!,{k,0,6n-p}],{p,1,6n}],{n,1,10}] (* Indranil Ghosh, Mar 04 2017 *)

PARI

a(n) = (6!^n)*sum(p=1,6*n,binomial(p,6)^n/p! * sum(k=0,6*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=6.