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 A385308 #16 Jun 28 2025 03:58:24
%S A385308 1,1,3,18,141,1400,17055,245392,4070073,76483584,1606033755,
%T A385308 37267953536,947051118981,26156846230528,780174007426359,
%U A385308 24992424003517440,855795857724702705,31193844533488074752,1205893835653392258867,49280187764171870470144,2122704756621224015194365
%N A385308 Expansion of e.g.f. 1/(1 - 2 * x * cosh(x))^(1/2).
%F A385308 a(n) = Sum_{k=0..n} A001147(k) * A185951(n,k), where A185951(n,0) = 0^n.
%F A385308 a(n) ~ sqrt(2) * n^n / (sqrt(1 + r*sqrt(1 - 4*r^2)) * exp(n) * r^n), where r = 0.452787214835453627588998503316635625709288535855... is the root of the equation 2*r*cosh(r) = 1. - _Vaclav Kotesovec_, Jun 28 2025
%o A385308 (PARI) a185951(n, k) = binomial(n, k)/2^k*sum(j=0, k, (2*j-k)^(n-k)*binomial(k, j));
%o A385308 a001147(n) = prod(k=0, n-1, 2*k+1);
%o A385308 a(n) = sum(k=0, n, a001147(k)*a185951(n, k));
%Y A385308 Cf. A205571, A385309.
%Y A385308 Cf. A380015, A385304, A385306, A385310.
%Y A385308 Cf. A001147, A185951, A352648, A385281.
%K A385308 nonn
%O A385308 0,3
%A A385308 _Seiichi Manyama_, Jun 24 2025