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 A126152 #16 Jan 26 2025 16:30:04
%S A126152 1,4,36,744,28536,1736064,152914176,18372559104,2885671339776,
%T A126152 573765893121024,140835811776316416,41820352964911908864,
%U A126152 14774712204104658671616,6124078747943873540112384
%N A126152 Main diagonal of symmetric triangle A126150: a(n) = A126150(n,n).
%H A126152 Vaclav Kotesovec, <a href="/A126152/b126152.txt">Table of n, a(n) for n = 0..232</a>
%F A126152 a(n) = Sum_{k=0..n} A130847(n,k)*3^k. - _Philippe Deléham_, Jul 22 2007
%F A126152 G.f.: 1/(1 - 4*x/(1 - 5*x/(1 - 21*x/(1 - 22*x/(1 - 50*x/(1 - 51*x/(1 - 91*x/(1 - 92*x/(1 -...))))))))), a continued fraction involving even-indexed pentagonal numbers A000326. - _Paul D. Hanna_, Feb 15 2012
%F A126152 a(n) ~ Gamma(1/3) * 2^(3*n+7/3) * 3^(n+3/2) * n^(2*n+7/6) / (exp(2*n) * Pi^(2*n+13/6)). - _Vaclav Kotesovec_, May 30 2015
%o A126152 (PARI) /* Continued fraction involving even-indexed pentagonal numbers: */
%o A126152 {a(n)=local(CF=1+x*O(x),m,P); for(k=1, n,m=2*((n-k)\2+1);P=m*(3*m-1)/2-((n-k+1)%2); CF=1/(1-P*x*CF)); polcoeff(CF, n, x)}
%o A126152 for(n=0,20,print1(a(n),","))
%Y A126152 Cf. A126150; A126151 (column 0), A126153 (diagonal).
%K A126152 nonn
%O A126152 0,2
%A A126152 _Paul D. Hanna_, Dec 19 2006