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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

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OFFSET

1,2

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=6.

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 *)

PROG

(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