login
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.
4
1, 209, 163121, 326922081, 1346634725665, 9939316337679281, 119802044788535500753, 2205421644124274191535553, 58945667435045762187763602753, 2198513228897522394476415669503377, 110833342180980170285766876408530089329, 7356710448423295420590529054176924329802529, 628972339934967292421997567343442748145219556449
OFFSET
1,2
COMMENTS
Apparently a duplicate of A071379? - R. J. Mathar, Mar 06 2017
FORMULA
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.
MATHEMATICA
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 *)
PROG
(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
CROSSREFS
KEYWORD
nonn
AUTHOR
Marko Riedel, Mar 01 2017
EXTENSIONS
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
STATUS
approved