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 A372316 #14 Feb 16 2025 08:34:06
%S A372316 1,2,10,125,2644,77597,2904382,132169403,7083715240,437031850841,
%T A372316 30506442905194,2377038378159359,204521399708464252,
%U A372316 19259006462435865413,1970114326513629358654,217556451608123850352523,25794252755430105917806288,3268152272130255473300883377
%N A372316 Expansion of e.g.f. exp( x - LambertW(-3*x)/3 ).
%H A372316 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LambertW-Function.html">Lambert W-Function</a>.
%F A372316 a(n) = Sum_{k=0..n} (3*k+1)^(k-1) * binomial(n,k).
%F A372316 G.f.: Sum_{k>=0} (3*k+1)^(k-1) * x^k / (1-x)^(k+1).
%F A372316 a(n) ~ 3^(n-1) * n^(n-1) * exp((exp(-1) + 1)/3). - _Vaclav Kotesovec_, May 04 2024
%o A372316 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(x-lambertw(-3*x)/3)))
%o A372316 (PARI) a(n) = sum(k=0, n, (3*k+1)^(k-1)*binomial(n, k));
%Y A372316 Cf. A088957, A360193, A372315, A372320, A372321.
%Y A372316 Cf. A362734.
%K A372316 nonn
%O A372316 0,2
%A A372316 _Seiichi Manyama_, Apr 27 2024