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 A060856 #22 Jun 23 2022 12:03:08 %S A060856 1,14,6006,140229804,278607172289160,67867669180627125604080, %T A060856 2760171874087743799855959353857200, %U A060856 24486819823897171791550434989846505231774984000,59986874261544072491135645330451363110127974096720977464312000 %N A060856 Multi-dimensional Catalan numbers: diagonal T(n,n+2) of A060854. %H A060856 G. C. Greubel, <a href="/A060856/b060856.txt">Table of n, a(n) for n = 1..29</a> %F A060856 a(n) = 0!*1!*...*(k-1)! *(k*n)! / ( n!*(n+1)!*...*(n+k-1)! ) for k=n+2. %F A060856 a(n) ~ sqrt(Pi) * exp(n^2/2 + 2*n + 25/12) * n^(n^2 + 2*n + 11/12) / (A * 2^(2*n^2 + 4*n + 17/12)), where A = A074962 = 1.2824271291... is the Glaisher-Kinkelin constant. - _Vaclav Kotesovec_, Mar 09 2015 %F A060856 a(n) = A039622(n+1) / (n+1). - _Tom Copeland_, May 30 2022 %t A060856 Table[Product[j!/(n+j)!,{j,0,n+1}]*(n*(n+2))!,{n,1,10}] (* _Vaclav Kotesovec_, Mar 09 2015 *) %Y A060856 Cf. A060854, A074962. %Y A060856 Cf. A039622. %K A060856 nonn,easy %O A060856 1,2 %A A060856 _R. H. Hardin_, May 03 2001