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 A385282 #14 Jun 26 2025 07:39:54
%S A385282 1,1,4,55,712,11605,248320,6218443,178519936,5846857993,214490045440,
%T A385282 8700546508159,387053184719872,18737207168958109,980424546959183872,
%U A385282 55142056940797803475,3317502712746788945920,212592531182720568805777,14456626429227650204041216
%N A385282 Expansion of e.g.f. 1/(1 - 3 * x * cosh(3*x))^(1/3).
%F A385282 a(n) = Sum_{k=0..n} A007559(k) * 3^(n-k) * A185951(n,k), where A185951(n,0) = 0^n.
%F A385282 a(n) ~ sqrt(2*Pi) * 3^n * n^(n - 1/6) / (Gamma(1/3) * (1/r + sqrt(1 - r^2))^(1/3) * exp(n) * r^(n + 1/3)), where r = A069814. - _Vaclav Kotesovec_, Jun 24 2025
%o A385282 (PARI) a185951(n, k) = binomial(n, k)/2^k*sum(j=0, k, (2*j-k)^(n-k)*binomial(k, j));
%o A385282 a007559(n) = prod(k=0, n-1, 3*k+1);
%o A385282 a(n) = sum(k=0, n, a007559(k)*3^(n-k)*a185951(n, k));
%Y A385282 Cf. A205571, A385281.
%Y A385282 Cf. A007559, A185951.
%Y A385282 Cf. A069814.
%K A385282 nonn
%O A385282 0,3
%A A385282 _Seiichi Manyama_, Jun 24 2025