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 A385307 #13 Jun 28 2025 03:43:11
%S A385307 1,1,4,27,264,3361,52704,981707,21176704,519150241,14255163904,
%T A385307 433384277787,14451212550144,524406240059521,20572970822959104,
%U A385307 867641565719168267,39145118179183427584,1881294510800399083201,95950279080398196834304,5176039012712211526485147
%N A385307 Expansion of e.g.f. 1/(1 - 3 * sin(x))^(1/3).
%F A385307 a(n) = Sum_{k=0..n} A007559(k) * i^(n-k) * A136630(n,k), where i is the imaginary unit.
%F A385307 a(n) ~ n! / (sqrt(2) * Gamma(1/3) * n^(2/3) * arcsin(1/3)^(n + 1/3)). - _Vaclav Kotesovec_, Jun 28 2025
%o A385307 (PARI) a136630(n, k) = 1/(2^k*k!)*sum(j=0, k, (-1)^(k-j)*(2*j-k)^n*binomial(k, j));
%o A385307 a007559(n) = prod(k=0, n-1, 3*k+1);
%o A385307 a(n) = sum(k=0, n, a007559(k)*I^(n-k)*a136630(n, k));
%Y A385307 Cf. A000111, A385306.
%Y A385307 Cf. A380017, A385305, A385309, A385311.
%Y A385307 Cf. A007559, A007788, A136630.
%K A385307 nonn
%O A385307 0,3
%A A385307 _Seiichi Manyama_, Jun 24 2025