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 A374882 #53 Feb 16 2025 08:34:07
%S A374882 1,1,7,109,2665,88981,3768391,193406977,11663021329,808092594505,
%T A374882 63252127883431,5519514702282901,531266903931402937,
%U A374882 55912682968563924829,6387276499619184590695,787104141893585220839401,104074098535487279656795681,14697203663694095986066104337
%N A374882 Expansion of e.g.f. exp( (1 - (1 - 9*x)^(1/3))/3 ).
%H A374882 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/BellPolynomial.html">Bell Polynomial</a>.
%F A374882 a(n) = Sum_{k=0..n} (-9)^(n-k) * Stirling1(n,k) * A317996(k) = (-9)^n * Sum_{k=0..n} (1/3)^k * Stirling1(n,k) * Bell_k(-1/3), where Bell_n(x) is n-th Bell polynomial.
%F A374882 From _Vaclav Kotesovec_, Aug 02 2024: (Start)
%F A374882 a(n) = 18*(n-2)*a(n-1) - 9*(3*n-8)*(3*n-7)*a(n-2) + a(n-3).
%F A374882 a(n) ~ Gamma(1/3) * 3^(2*n - 3/2) * n^(n - 5/6) / (sqrt(2*Pi) * exp(n - 1/3)) * (1 - 2*Pi/(3^(3/2)*Gamma(1/3)^2*n^(1/3))). (End)
%o A374882 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp((1-(1-9*x)^(1/3))/3)))
%Y A374882 Cf. A080893, A252284, A317996.
%Y A374882 Cf. A375174, A375176.
%K A374882 nonn
%O A374882 0,3
%A A374882 _Seiichi Manyama_, Aug 02 2024