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 A362381 #18 Feb 16 2025 08:34:05
%S A362381 1,1,1,2,9,41,191,1191,9353,77897,704861,7352621,85323921,1058023825,
%T A362381 14155416003,206100005931,3217934262481,53320102598481,
%U A362381 939087824434009,17562552535939705,346668611080774081,7196193133818592961,156944931623033340711
%N A362381 E.g.f. satisfies A(x) = exp(x + x^3/6 * A(x)).
%H A362381 Seiichi Manyama, <a href="/A362381/b362381.txt">Table of n, a(n) for n = 0..447</a>
%H A362381 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LambertW-Function.html">Lambert W-Function</a>.
%F A362381 E.g.f.: exp(x - LambertW(-x^3/6 * exp(x))) = -6 * LambertW(-x^3/6 * exp(x))/x^3.
%F A362381 a(n) = n! * Sum_{k=0..floor(n/3)} (1/6)^k * (k+1)^(n-2*k-1) / (k! * (n-3*k)!).
%o A362381 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x-lambertw(-x^3/6*exp(x)))))
%Y A362381 Column k=1 of A362378.
%Y A362381 Cf. A190865, A362477.
%K A362381 nonn
%O A362381 0,4
%A A362381 _Seiichi Manyama_, Apr 20 2023