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 A385281 #15 Jun 26 2025 07:41:17
%S A385281 1,1,3,27,249,2825,41355,708883,13888497,309267729,7698772755,
%T A385281 211585744139,6367841422569,208299923870233,7357493992966299,
%U A385281 279095125351544835,11316313498670411745,488403056864943302177,22355228989851909617187,1081663315375339026249211
%N A385281 Expansion of e.g.f. 1/(1 - 2 * x * cosh(2*x))^(1/2).
%F A385281 a(n) = Sum_{k=0..n} A001147(k) * 2^(n-k) * A185951(n,k), where A185951(n,0) = 0^n.
%F A385281 a(n) ~ 2^(n + 1/2) * n^n / (sqrt(1 + r*sqrt(1 - r^2)) * exp(n) * r^n), where r = A069814. - _Vaclav Kotesovec_, Jun 24 2025
%o A385281 (PARI) a185951(n, k) = binomial(n, k)/2^k*sum(j=0, k, (2*j-k)^(n-k)*binomial(k, j));
%o A385281 a001147(n) = prod(k=0, n-1, 2*k+1);
%o A385281 a(n) = sum(k=0, n, a001147(k)*2^(n-k)*a185951(n, k));
%Y A385281 Cf. A205571, A385282.
%Y A385281 Cf. A001586, A235134, A380155, A385283.
%Y A385281 Cf. A001147, A185951.
%Y A385281 Cf. A069814.
%K A385281 nonn
%O A385281 0,3
%A A385281 _Seiichi Manyama_, Jun 24 2025