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 A375174 #13 Feb 16 2025 08:34:07
%S A375174 1,1,13,289,9073,367681,18249661,1071805393,72684954049,5588943933313,
%T A375174 480445784729101,45656401249018561,4752397230972673393,
%U A375174 537724197016879848769,65711109523289467682173,8624825762253351871394161,1210085772867351648907603201
%N A375174 Expansion of e.g.f. exp( (1/(1 - 9*x)^(1/3) - 1)/3 ).
%H A375174 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/BellPolynomial.html">Bell Polynomial</a>.
%F A375174 a(n) = Sum_{k=0..n} 9^(n-k) * |Stirling1(n,k)| * A004212(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 A375174 From _Vaclav Kotesovec_, Aug 02 2024: (Start)
%F A375174 a(n) = 36*(n-2)*a(n-1) - 18*(27*n^2 - 135*n + 172)*a(n-2) + (2916*n^3 - 26244*n^2 + 79056*n - 79703)*a(n-3) - 729*(n-4)*(n-3)*(3*n - 11)*(3*n - 10)*a(n-4).
%F A375174 a(n) ~ 3^(2*n - 1/4) * n^(n - 3/8) / (2*exp(n - 4*n^(1/4)/3^(3/2) + 1/3)) * (1 - 35/(32*sqrt(3)*n^(1/4))). (End)
%o A375174 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp((1/(1-9*x)^(1/3)-1)/3)))
%Y A375174 Cf. A374882, A375176.
%Y A375174 Cf. A004212.
%K A375174 nonn
%O A375174 0,3
%A A375174 _Seiichi Manyama_, Aug 02 2024