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 A135438 #24 Jan 04 2023 05:10:25
%S A135438 1,1,5,70,2100,115500,10510500,1471470000,300179880000,85551265800000,
%T A135438 32937237333000000,16666242090498000000,10833057358823700000000,
%U A135438 8872273976876610300000000,9005358086529759454500000000,11166644027296901723580000000000,16705299464836164978475680000000000,29818959544732554486579088800000000000
%N A135438 Denominators (numerators are all 1) of the series: 1/1^2, (1/1^2)*(1/(1^2+2^2)), (1/1^2)*(1/(1^2+2^2))*(1/(1^2+2^2+3^2)), ...
%C A135438 The series converges to hypergeom([1], [2, 5/2, 3], 3). The sum is the Engels expansions of the limit. The n-th fraction is 12^n / ( (n+1)! (2n+1)! ). The denominators are given by (n+1)!*(2*n+1)!/12^n.
%C A135438 Terms of this sequence for n>= 1 are products of factors of consecutive terms of A000330.
%C A135438 10^floor(n/3)|a(n). - _G. C. Greubel_, Oct 14 2016
%H A135438 G. C. Greubel, <a href="/A135438/b135438.txt">Table of n, a(n) for n = 0..100</a>
%F A135438 a(n) = (n+1)!*(2*n+1)!/12^n.
%t A135438 Table[(n + 1)! (2 n + 1)!/12^n, {n, 0, 25}] (* _G. C. Greubel_, Oct 14 2016 *)
%o A135438 (PARI) a(n) = (n+1)!*(2*n+1)!/12^n
%Y A135438 Cf. A000330.
%K A135438 nonn
%O A135438 0,3
%A A135438 _Alexander R. Povolotsky_, Dec 14 2007
%E A135438 Edited by _N. J. A. Sloane_, Dec 14 2007