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 A378017 #9 Feb 16 2025 08:34:07
%S A378017 1,3,15,148,2077,38326,883369,24431436,789531705,29213730010,
%T A378017 1218401262541,56566561281616,2893886178904549,161768999193007974,
%U A378017 9811122121462081281,641683497800057913556,45022670799746182036465,3373421864644139722767538,268843153008388446079159573
%N A378017 E.g.f. satisfies A(x) = (1+x)^2 * exp( x * (1+x) * A(x) ).
%H A378017 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LambertW-Function.html">Lambert W-Function</a>.
%F A378017 E.g.f.: (1+x)^2 * exp( -LambertW(-x * (1+x)^3) ).
%F A378017 a(n) = n! * Sum_{k=0..n} (k+1)^(k-1) * binomial(3*k+2,n-k)/k!.
%o A378017 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace((1+x)^2*exp(-lambertw(-x*(1+x)^3))))
%o A378017 (PARI) a(n) = n!*sum(k=0, n, (k+1)^(k-1)*binomial(3*k+2, n-k)/k!);
%Y A378017 Cf. A376145, A377828, A378016.
%Y A378017 Cf. A377966.
%K A378017 nonn
%O A378017 0,2
%A A378017 _Seiichi Manyama_, Nov 14 2024