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 A172492 #11 Apr 22 2024 07:34:38 %S A172492 1,2,24,864,69120,10368000,2612736000,1024192512000,589934886912000, %T A172492 477847258398720000,525631984238592000000,763217641114435584000000, %U A172492 1428743424166223413248000000,3380406941577284595744768000000 %N A172492 a(n) = (n!)^2*(n+1)!. %C A172492 Asymptotics: a(n)->(1/16)*Pi^(3/2)*sqrt(2)*(32*n^2+40*n+9)*exp(-3*n)*(n)^(1/2+3*n), n->infinity. %F A172492 Generating function of hypergeometric type, in Maple notation: sum(a(n)*x^n/(n!)^3, n=0..infinity)=1/(1-x)^2. %F A172492 Integral representation as n-th moment of a positive function on a positive half-axis (solution of the Stieltjes moment problem), in Maple notation: a(n)=int(x^n*MeijerG([[],[]],[[0,0,1],[]],x),x=0..infinity), n=0,1... . %F A172492 The MeijerG function above cannot be represented by any other known special function. %F A172492 This solution of the Stieltjes moment problem is not unique. %o A172492 (Python) %o A172492 from math import factorial %o A172492 def A172492(n): return factorial(n)**3*(n+1) # _Chai Wah Wu_, Apr 22 2024 %K A172492 nonn %O A172492 0,2 %A A172492 _Karol A. Penson_, Feb 05 2010