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 A385719 #32 Aug 20 2025 05:55:11
%S A385719 1,4,38,428,5204,66104,863840,11515308,155779966,2131436392,
%T A385719 29426804398,409254436452,5726378247412,80535621269208,
%U A385719 1137609359823936,16130112288879248,229462608491483364,3273749607191060480,46826932120849617128,671341041479214814160,9644654058165119642624
%N A385719 Expansion of B(x)/sqrt(1 + 2*(B(x)-1)/3), where B(x) is the g.f. of A004355.
%H A385719 Vaclav Kotesovec, <a href="/A385719/b385719.txt">Table of n, a(n) for n = 0..850</a>
%F A385719 Sum_{k=0..n} a(k) * a(n-k) = A385497(n).
%F A385719 G.f.: 1/sqrt(1 - 4*x*g^4*(3-g)) where g = 1+x*g^6 is the g.f. of A002295.
%F A385719 G.f.: g/sqrt((2-g) * (6-5*g)) where g = 1+x*g^6 is the g.f. of A002295.
%F A385719 a(n) ~ 2^(6*n - 1/2) * 3^(6*n + 3/4) / (Gamma(1/4) * n^(3/4) * 5^(5*n + 1/4)) * (1 + 7*Gamma(1/4)^2/(48*Pi*sqrt(30*n))). - _Vaclav Kotesovec_, Aug 20 2025
%t A385719 nmax = 20; CoefficientList[Series[Sum[Binomial[6*n, n]*x^n, {n, 0, nmax}] / Sqrt[1 + 2*(Sum[Binomial[6*n, n]*x^n, {n, 0, nmax}] - 1)/3], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Aug 20 2025 *)
%Y A385719 Cf. A183161, A208977, A387084, A387086.
%Y A385719 Cf. A002295, A004355, A385497.
%K A385719 nonn
%O A385719 0,2
%A A385719 _Seiichi Manyama_, Aug 17 2025