A107251 - OEIS

%I #11 Feb 19 2019 03:45:05

%S 1,1,12,7200,508032000,7742895390720000,40797452088662556672000000,

%T 108985983996792124183843071590400000000,

%U 203800994173724454677862841368011757060096000000000000

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

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

%F 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

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

%p seq(mul(mul(k+j,j=1..n), k=2..n), n=0..8); # _Zerinvary Lajos_, Jun 01 2007

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

%Y Cf. A000142, A000178, A079478.

%K nonn

%O 0,3

%A _Henry Bottomley_, May 14 2005