A172710 Number of 7*n X 2*n 0..2 arrays with row sums 2 and column sums 7.

393, 492872166072, 737005538936597762145600, 117847210656873992022720603629873856000, 620630259068078856134953474839665823595181960916480000

Offset

1,1

Links

R. H. Hardin, Table of n, a(n) for n = 1..14

Formula

a(n) = ((2n)!(7n)!/(7!)^(2n)) Sum_{i=0..2n} Sum_{j=0..2n-i} Sum_{k=0..2n-i-j} (21^j*105^(2n-i-j)*(6i+4j+2k+2n)!/(i!j!k!(2n-i-j-k)!(n+2j+k+3i)!*2^(n+2j+k+3i))). - Shanzhen Gao, Feb 24 2010

a(n) ~ sqrt(Pi) * 7^(12*n + 1/2) * n^(14*n + 1/2) / (2^(n-1) * 3^(4*n) * 5^(2*n) * exp(14*n-3)). - Vaclav Kotesovec, Oct 22 2023

Mathematica

Table[(2*n)!*(7*n)!/(7!)^(2*n) * Sum[Sum[Sum[(21^j*105^(2*n-i-j)*(6*i+4*j+2*k+2*n)! / (i!*j!*k!*(2*n-i-j-k)!*(n+2*j+k+3*i)! * 2^(n+2*j+k+3*i))), {k, 0, 2*n-i-j}], {j, 0, 2*n-i}], {i, 0, 2*n}], {n, 1, 12}] (* Vaclav Kotesovec, Oct 22 2023 *)

Prog

(PARI) a(n) = ((2*n)!*(7*n)!/(7!)^(2*n))*sum(i=0, 2*n, sum(j=0, 2*n-i, sum(k=0, 2*n-i-j, (21^j*105^(2*n-i-j)*(6*i+4*j+2*k+2*n)!/(i!*j!*k!*(2*n-i-j-k)!*(n+2*j+k+3*i)!*2^(n+2*j+k+3*i)))))); \\ Michel Marcus, Jan 17 2018

Crossrefs

Sequence in context: A172872 A172903 A172931 * A236234 A252691 A051986

Adjacent sequences: A172707 A172708 A172709 * A172711 A172712 A172713

Keyword

nonn

Author

R. H. Hardin, Feb 06 2010

Status

approved