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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.

%I A283153 #29 Feb 02 2019 02:32:59
%S A283153 1,209,163121,326922081,1346634725665,9939316337679281,
%T A283153 119802044788535500753,2205421644124274191535553,
%U A283153 58945667435045762187763602753,2198513228897522394476415669503377,110833342180980170285766876408530089329,7356710448423295420590529054176924329802529,628972339934967292421997567343442748145219556449
%N 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.
%C A283153 Apparently a duplicate of A071379? - _R. J. Mathar_, Mar 06 2017
%H A283153 Indranil Ghosh, <a href="/A283153/b283153.txt">Table of n, a(n) for n = 1..50</a>
%H A283153 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>
%H A283153 Marko Riedel, <a href="/A283153/a283153_1.maple.txt">Maple code for generalized Bell numbers, A000110, A020556, A069223, A283153, A283154, A283155, optimized version</a>
%F A283153 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.
%t A283153 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 *)
%o A283153 (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
%Y A283153 Cf. A283154, A283155, A071379.
%K A283153 nonn
%O A283153 1,2
%A A283153 _Marko Riedel_, Mar 01 2017
%E A283153 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