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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.
4
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
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
Sequence in context: A249473 A246899 A090209 * A157347 A255356 A336221
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