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 A368545 #9 Dec 29 2023 09:51:06
%S A368545 1,1512,13477464,156037527360,2018989675062360,27791880541579666512,
%T A368545 397974308267103144857280,5857301482132559510090140920,
%U A368545 87960819866039245485380114158680,1341476995616395775866469804150505600,20709814202640945368698086671062023292464,322897098547446926110838713561401344838974976
%N A368545 a(n) = (6*n)!*(9*n)!/((2*n)!*(3*n)!*((5*n)!)^2).
%F A368545 G.f.: hypergeometric10F9([1/9, 1/6, 2/9, 1/3, 4/9, 5/9, 2/3, 7/9, 5/6, 8/9], [1/5, 1/5, 2/5, 2/5, 3/5, 3/5, 4/5, 4/5, 1], (167365651248*z)/9765625).
%F A368545 E.g.f.: hypergeometric10F10([1/9, 1/6, 2/9, 1/3, 4/9, 5/9, 2/3, 7/9, 5/6, 8/9], [1/5, 1/5, 2/5, 2/5, 3/5, 3/5, 4/5, 4/5, 1,1], (167365651248*z)/9765625).
%F A368545 a(n) = Integral_{x=0..167365651248/9765625} x^n*W(x) dx, n>=0, where W(x) = (1953125*MeijerG([[], [-4/5, -4/5, -3/5, -3/5, -2/5, -2/5, -1/5, -1/5, 0, 0]], [[-1/9, -1/6, -2/9, -1/3, -4/9, -5/9, -2/3, -7/9, -5/6, -8/9], []], (9765625*x)/167365651248))/(111577100832*Pi). MeijerG is the Meijer G - function. This integral representation as the n-th power moment of the W(x) function in the interval [0, 167365651248/9765625] is verified by direct integration. However, we are unable at present to determine the geometric shape of W(x).
%p A368545 seq((6*n)!*(9*n)!/((2*n)!*(3*n)!*((5*n)!)^2),n=0..12);
%Y A368545 Cf. A113424, A368513, A304126.
%K A368545 nonn
%O A368545 0,2
%A A368545 _Karol A. Penson_, Dec 29 2023