A152296 Let f(M,N)=2^(-M)*sum_{i=0..N} {(-1)^{i}M!N!(2M-2i)!}/{i!(M-i)!(N-i)!6^{N-i}}; then a(n) = f(3n,n).

1, 6, 113400, 32901422400, 67651716132000000, 608762379843757339200000, 17903325789347617610786995200000, 1415199921956087613201896962521600000000, 261375521452474271183649591888039276441600000000, 101519644940256627137917269623207295713536128000000000000, 76392226231236455854222646891536244623780022885776896000000000000

Offset

0,2

Links

Table of n, a(n) for n=0..10.

Formula

a(n) ~ sqrt(Pi) * 2^(2*n+1) * 3^(5*n + 1/2) * n^(6*n + 1/2) / exp(6*n + 1/2). - Vaclav Kotesovec, Oct 21 2023

Mathematica

Table[2^(-3*n) * Sum[(-1)^i * (3*n)! * n! * (6*n-2*i)! / (i! * (3*n-i)! * (n-i)! * 6^(n-i)), {i, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Oct 21 2023 *)
Table[(6*n)! * Hypergeometric1F1[-n, 1/2 - 3*n, -3/2] / (2^(4*n) * 3^n), {n, 0, 20}] (* Vaclav Kotesovec, Oct 21 2023 *)

Crossrefs

A variant of A132202. Cf. A134648, A134772, A152296.

Sequence in context: A086897 A034208 A003834 * A358811 A076909 A172864

Adjacent sequences: A152293 A152294 A152295 * A152297 A152298 A152299

Keyword

nonn

Author

N. J. A. Sloane, Oct 18 2009

Status

approved