A049504 a(n) = Product_{i = 0..n-1} ((3*i+1)!*(6*i)!*(2*i)!)/((4*i)!*(4*i+1)!).

1, 1, 12, 47520, 266499072000, 5578457158440714240000, 903833169262981594760400076800000000, 2035652583056655211566004660439314466655436800000000000, 103962610930356904475854868257296244089884364267142052118842572800000000000000

Offset

0,3

Comments

Given in first printing of Bressoud book as number of cyclically symmetric transpose complement plane partitions. For correct version see A051255.

References

D. M. Bressoud, Proofs and Confirmations, Camb. Univ. Press, 1999; Eq. (6.15), p. 199.

Links

Table of n, a(n) for n=0..8.

Formula

a(n) ~ A^(-1/2) * Gamma(1/3) * 2^(-1/9 + 3*n/2 - 4*n^2) * 3^(-1/24 - 5*n/2 + 9*n^2/2) * exp(1/24 + n - 9*n^2/4) * n^(1/8 - n + 3*n^2/2) * Pi^((n-1)/2), where A = A074962 is the Glaisher-Kinkelin constant. - Vaclav Kotesovec, Apr 25 2016

Maple

a := proc(n) local i; mul((3*i+1)!*(6*i)!*(2*i)!/((4*i)!*(4*i+1)!), i = 0..n-1); end;

Mathematica

Table[Product[((3i+1)!(6i)!(2i)!)/((4i)!(4i+1)!), {i, 0, n-1}], {n, 0, 10}] (* Harvey P. Dale, Apr 25 2016 *)

Crossrefs

Sequence in context: A220791 A146519 A277693 * A308374 A134714 A127223

Adjacent sequences: A049501 A049502 A049503 * A049505 A049506 A049507

Keyword

nonn,nice,easy

Author

N. J. A. Sloane

Extensions

Definition corrected by Harvey P. Dale, Apr 25 2016

Status

approved