A172597 Number of 6*n X n 0..1 arrays with row sums 2 and column sums 12

0, 1, 17153136, 25780447171287900, 674741194624071430134879600, 181567587344159723781226957237357470000, 346851737504423205666773757122219688261768787084800

Offset

1,3

References

Gao, Shanzhen, and Matheis, Kenneth, Closed formulas and integer sequences arising from the enumeration of (0,1)-matrices with row sum two and some constant column sums. In Proceedings of the Forty-First Southeastern International Conference on Combinatorics, Graph Theory and Computing. Congr. Numer. 202 (2010), 45-53.

Links

Vaclav Kotesovec, Table of n, a(n) for n = 1..55 (terms 1..15 from R. H. Hardin)

Formula

a(n) = ((6n)!n!/2^(6n))* Sum_{i=0..n} Sum_{j=0..n-i} Sum_{k=0..n-i-j} Sum_{m=0..n-i-j-k} Sum_{u=0..n-i-j-k-m} Sum_{v=0..n-i-j-k-m-u} (1/(i!j!k!m!u!v!(n-i-j-k-m-u-v)!))*((-1)^(-5j-4k-3m-2u-v+6n-6i)/(6n+5j+4k+3m+2u+v-6n+6i)!)*((12i+10j+8k+6m+4u+2v)!/(12!^i*10!^j*(2!8!)^k*(3!6!)^m*(4!4!)^u*(5!2!)^v*6!^(n-i-j-k-m-u-v))). - Shanzhen Gao, Feb 18 2010

a(n) ~ sqrt(Pi) * 2^(8*n + 3/2) * 3^(7*n + 1/2) * n^(12*n + 1/2) / (5^(2*n) * 7^n * 11^n * exp(12*n + 11/2)). - Vaclav Kotesovec, Oct 23 2023

Mathematica

Table[(6*n)!*n!/2^(6*n) * Sum[Sum[Sum[Sum[Sum[Sum[(1/(i!*j!*k!*m!*u!*v!*(n-i-j-k-m-u-v)!)) * ((-1)^(-5*j-4*k-3*m-2*u-v+6*n-6*i)/(6*n+5*j+4*k+3*m+2*u+v-6*n+6*i)!) * ((12*i+10*j+8*k+6*m+4*u+2*v)! / (12!^i*10!^j*(2!8!)^k*(3!6!)^m*(4!4!)^u*(5!2!)^v * 6!^(n-i-j-k-m-u-v))), {v, 0, n-i-j-k-m-u}], {u, 0, n-i-j-k-m}], {m, 0, n-i-j-k}], {k, 0, n-i-j}], {j, 0, n-i}], {i, 0, n}], {n, 1, 12}] (* Vaclav Kotesovec, Oct 22 2023 *)

Crossrefs

Sequence in context: A204673 A205640 A175271 * A172569 A254000 A129478

Adjacent sequences: A172594 A172595 A172596 * A172598 A172599 A172600

Keyword

nonn

Author

R. H. Hardin, Feb 06 2010

Status

approved