A107251 Supercatalan numbers SF(2n)/(SF(n)*SF(n+1)) where SF is the superfactorial function A000178.

1, 1, 12, 7200, 508032000, 7742895390720000, 40797452088662556672000000, 108985983996792124183843071590400000000, 203800994173724454677862841368011757060096000000000000

Offset: 0

Author

Henry Bottomley, May 14 2005

Keywords

• nonn

Examples

			a(3) = 1!*2!*3!*4!*5!*6!/(1!*2!*3!*1!*2!*3!*4!) = 24883200/(12*288) = 7200.
		

Crossrefs

Cf. A000108 for original Catalan numbers (2n)!/(n!*(n+1)!).

Cf. A000142, A000178, A079478.

Programs

Maple

seq(mul(mul(k+j,j=1..n), k=2..n), n=0..8); # Zerinvary Lajos, Jun 01 2007

Formula

a(n) = (n+2)!*(n+3)!*...*(2n)!/(2!*3!*...*n!) = A000178(2n)/(A000178(n)*A000178(n+1)) = A079478(n)/A000142(n+1).

a(n) ~ A * 2^(2*n^2 + 2*n - 7/12) * n^(n^2 - n - 23/12) / (Pi * exp(3*n^2/2 - n + 1/12)), where A = A074962 = 1.2824271291... is the Glaisher-Kinkelin constant. - Vaclav Kotesovec, Jul 10 2015