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 A383627 #17 Aug 18 2025 05:38:04
%S A383627 1,4,19,100,562,3304,20062,124744,789553,5065444,32840347,214681636,
%T A383627 1412786872,9348241504,62138211112,414627600736,2775808278058,
%U A383627 18636412183336,125436195473662,846145250012776,5719044971926972,38723124875350960,262609593669266404
%N A383627 Expansion of 1/( Product_{k=0..2} (1 - (3*k+1) * x) )^(1/3).
%C A383627 In general, if m > 0 and g.f. = 1/(Product_{k=0..m-1} (1 - (m*k+1)*x))^(1/m), then a(n) ~ (m*(m-1) + 1)^(n + 1 - 1/m) / (Gamma(1/m) * Gamma(m+1)^(1/m) * m^(1 - 2/m) * n^(1 - 1/m)). - _Vaclav Kotesovec_, Aug 18 2025
%F A383627 a(n) ~ 7^(n + 2/3) / (Gamma(1/3) * 2^(1/3) * 3^(2/3) * n^(2/3)). - _Vaclav Kotesovec_, May 12 2025
%F A383627 a(n) = Sum_{k=0..n} binomial(n,k) * A383935(k). - _Seiichi Manyama_, Aug 18 2025
%o A383627 (PARI) my(N=30, x='x+O('x^N)); Vec(1/prod(k=0, 2, 1-(3*k+1)*x)^(1/3))
%Y A383627 Cf. A383628, A383629, A383630, A383631, A383632, A383633.
%Y A383627 Cf. A016223, A370781, A383935.
%K A383627 nonn
%O A383627 0,2
%A A383627 _Seiichi Manyama_, May 03 2025