This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A107251 #11 Feb 19 2019 03:45:05 %S A107251 1,1,12,7200,508032000,7742895390720000,40797452088662556672000000, %T A107251 108985983996792124183843071590400000000, %U A107251 203800994173724454677862841368011757060096000000000000 %N A107251 Supercatalan numbers SF(2n)/(SF(n)*SF(n+1)) where SF is the superfactorial function A000178. %F A107251 a(n) = (n+2)!*(n+3)!*...*(2n)!/(2!*3!*...*n!) = A000178(2n)/(A000178(n)*A000178(n+1)) = A079478(n)/A000142(n+1). %F A107251 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 A107251 a(3) = 1!*2!*3!*4!*5!*6!/(1!*2!*3!*1!*2!*3!*4!) = 24883200/(12*288) = 7200. %p A107251 seq(mul(mul(k+j,j=1..n), k=2..n), n=0..8); # _Zerinvary Lajos_, Jun 01 2007 %Y A107251 Cf. A000108 for original Catalan numbers (2n)!/(n!*(n+1)!). %Y A107251 Cf. A000142, A000178, A079478. %K A107251 nonn %O A107251 0,3 %A A107251 _Henry Bottomley_, May 14 2005