A072477 a(n) = (2*n)!*binomial(2*n,n)/8.

18, 1800, 352800, 114307200, 55324684800, 37399486924800, 33659538232320000, 38910426196561920000, 56186655427835412480000, 99113260174701667614720000, 209723658529668728672747520000, 524309146324171821681868800000000, 1528885470681285032024329420800000000

Offset

2,1

Links

Table of n, a(n) for n=2..14.

Michel Bousquet, Gilbert Labelle, and Pierre Leroux, Enumeration of planar two-face maps, Discrete Mathematics, 222 (2000), 1-25.

Formula

From Amiram Eldar, Jun 18 2025: (Start)

Sum_{n>=2} 1/a(n) = 2*Pi*L_0(1/2) - 2, where L is the modified Struve function.

Sum_{n>=2} (-1)^n/a(n) = 2 - 2*Pi*H_0(1/2), where H is the Struve function. (End)

a(n) ~ 4^(2*n-1) * (n/e)^(2*n). - Amiram Eldar, Oct 19 2025

Mathematica

a[n_] := (2*n)!*Binomial[2*n, n]/8; Array[a, 12, 2] (* Amiram Eldar, Jun 18 2025 *)

Prog

(PARI) a(n) = (2*n)!*binomial(2*n, n)/8; \\ Amiram Eldar, Jun 18 2025

Crossrefs

Cf. A000984, A122747.

Sequence in context: A253121 A067303 A055740 * A249332 A019522 A068181

Adjacent sequences: A072474 A072475 A072476 * A072478 A072479 A072480

Keyword

nonn,easy

Author

N. J. A. Sloane, Aug 02 2002

Status

approved