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 A380261 #14 Feb 16 2025 08:34:07
%S A380261 1,1,0,2,-14,146,-1944,31620,-608068,13502076,-340052704,9579145016,
%T A380261 -298455813160,10191129869272,-378469678855904,15187759126892976,
%U A380261 -654936026064200944,30203464484648818960,-1483333523694819075328,77291514214052885054496
%N A380261 Expansion of e.g.f. exp( ((1+3*x)^(2/3) - 1)/2 ).
%H A380261 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/BellPolynomial.html">Bell Polynomial</a>.
%F A380261 a(n) = Sum_{k=0..n} 3^(n-k) * Stirling1(n,k) * A004211(k) = Sum_{k=0..n} 2^k * 3^(n-k) * Stirling1(n,k) * Bell_k(1/2), where Bell_n(x) is n-th Bell polynomial.
%F A380261 a(n) = (1/exp(1/2)) * 3^n * n! * Sum_{k>=0} binomial(2*k/3,n)/(2^k * k!).
%o A380261 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(((1+3*x)^(2/3)-1)/2)))
%Y A380261 Cf. A000085, A002119, A004211, A380262.
%K A380261 sign
%O A380261 0,4
%A A380261 _Seiichi Manyama_, Jan 18 2025