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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.

%I A283154 #20 Mar 06 2017 20:04:13
%S A283154 1,1546,12962661,363303011071,25571928251231076,
%T A283154 3789505947767235111051,1049433111253356296672432821,
%U A283154 498382374325731085522315594481036,380385281554629647028734545622539438171,443499171330317702437047276255605780991365151,758311423589226886694849718263394302618332719358226
%N 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.
%C A283154 Apparently a duplicate of A090209. - _R. J. Mathar_, Mar 06 2017
%H A283154 Indranil Ghosh, <a href="/A283154/b283154.txt">Table of n, a(n) for n = 1..50</a>
%H A283154 M. Riedel, <a href="http://math.stackexchange.com/questions/2165093/">Set partitions of unique elements from an n-by-m matrix where elements from the same row may not be in the same partition</a>
%F A283154 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.
%t A283154 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 *)
%o A283154 (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
%Y A283154 Cf. A283153, A283155.
%K A283154 nonn
%O A283154 1,2
%A A283154 _Marko Riedel_, Mar 01 2017
%E A283154 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