A172678 Number of 4*n X n 0..2 arrays with row sums 2 and column sums 8.

1, 1107, 57775905, 40629560387130, 203571289613781911250, 4937928427617947420104982250, 447362835296127429187676764430583750, 125661678519106774927206307245894357500775000, 95131219937961621952706904277268129938808819520975000

Offset

1,2

Links

R. H. Hardin, Table of n, a(n) for n=1..24

Formula

a(n) = (1/(8!)^n)*Sum_{v=0..n} Sum_{m=0..n-v} Sum_{g=0..n-v-m} Sum_{b=0..n-v-m-g} (28^b*210^g*420^m*105^v*n!*(4*n)!*(8*n-2*b-4*g-6*m-8*v)!)/((n-b-g-m-v)!*b!*g!*m!*v!*(4*n-b-2*g-3*m-4*v)!*2^(4*n-b-2*g-3*m-4*v)). - Shanzhen Gao, Feb 25 2010

a(n) ~ sqrt(Pi) * 2^(13*n+2) * n^(8*n + 1/2) / (3^(2*n) * 5^n * 7^n * exp(8*n - 7/2)). - Vaclav Kotesovec, Oct 22 2023

Mathematica

Table[1/(8!)^n * Sum[Sum[Sum[Sum[(28^b*210^g*420^m*105^v*n!*(4*n)! * (8*n-2*b-4*g-6*m-8*v)!) / ((n-b-g-m-v)! * b!*g!*m!*v! * (4*n-b-2*g-3*m-4*v)! * 2^(4*n-b-2*g-3*m-4*v)), {b, 0, n-v-m-g}], {g, 0, n-v-m}], {m, 0, n-v}], {v, 0, n}], {n, 1, 12}] (* Vaclav Kotesovec, Oct 22 2023 *)

Prog

(PARI) a(n) = (1/(8!)^n)*sum(v=0, n, sum(m=0, n-v, sum(g=0, n-v-m, sum(b=0, n-v-m-g, (28^b*210^g*420^m*105^v*n!*(4*n)!*(8*n-2*b-4*g-6*m-8*v)!)/((n-b-g-m-v)!*b!*g!*m!*v!*(4*n-b-2*g-3*m-4*v)!*2^(4*n-b-2*g-3*m-4*v)) )))) \\ Andrew Howroyd, Feb 07 2025

Crossrefs

Sequence in context: A172905 A172928 A172947 * A172774 A234156 A066163

Adjacent sequences: A172675 A172676 A172677 * A172679 A172680 A172681

Keyword

nonn

Author

R. H. Hardin, Feb 06 2010

Status

approved