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 A385311 #15 Jun 26 2025 08:08:42
%S A385311 1,1,4,25,232,2805,41920,744933,15340416,359136073,9419223040,
%T A385311 273558859409,8714789788672,302151400126589,11326084055150592,
%U A385311 456421403198919325,19677025400034590720,903660903945306053137,44042354270955276599296,2270411632567521580120713
%N A385311 Expansion of e.g.f. 1/(1 - 3 * x * cos(x))^(1/3).
%F A385311 a(n) = Sum_{k=0..n} A007559(k) * i^(n-k) * A185951(n,k), where i is the imaginary unit and A185951(n,0) = 0^n.
%o A385311 (PARI) a185951(n, k) = binomial(n, k)/2^k*sum(j=0, k, (2*j-k)^(n-k)*binomial(k, j));
%o A385311 a007559(n) = prod(k=0, n-1, 3*k+1);
%o A385311 a(n) = sum(k=0, n, a007559(k)*I^(n-k)*a185951(n, k));
%Y A385311 Cf. A352252, A385310.
%Y A385311 Cf. A380017, A385305, A385307, A385309.
%Y A385311 Cf. A007559, A185951, A352647, A385284.
%K A385311 nonn
%O A385311 0,3
%A A385311 _Seiichi Manyama_, Jun 24 2025