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 A372235 #34 Feb 16 2025 08:34:06
%S A372235 1,2,10,98,1456,29132,734932,22407464,801710560,32940601424,
%T A372235 1528816004944,79109107128944,4516145972879680,281970941337424640,
%U A372235 19114791434098402816,1398205517746364523008,109771912847021666795008,9206931548976575570314496
%N A372235 E.g.f. A(x) satisfies A(x) = exp( x * (1 + A(x)^(3/2)) ).
%H A372235 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LambertW-Function.html">Lambert W-Function</a>.
%F A372235 E.g.f.: A(x) = exp( x - 2/3 * LambertW(-3*x/2 * exp(3*x/2)) ).
%F A372235 If e.g.f. satisfies A(x) = exp( r*x*A(x)^(t/r) * (1 + A(x)^(u/r)) ), then a(n) = r * Sum_{k=0..n} (t*n+u*k+r)^(n-1) * binomial(n,k).
%F A372235 G.f.: Sum_{k>=0} (3*k/2+1)^(k-1) * x^k/(1 - (3*k/2+1)*x)^(k+1).
%F A372235 a(n) ~ sqrt(1 + LambertW(exp(-1))) * 3^(n-1) * n^(n-1) / (2^(n-1) * exp(n) * LambertW(exp(-1))^(n + 2/3)). - _Vaclav Kotesovec_, Apr 24 2024
%o A372235 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(x-2/3*lambertw(-3*x/2*exp(3*x/2)))))
%o A372235 (PARI) a(n, r=1, t=0, u=3/2) = r*sum(k=0, n, (t*n+u*k+r)^(n-1)*binomial(n, k));
%o A372235 (PARI) my(N=20, x='x+O('x^N)); Vec(sum(k=0, N, (3*k/2+1)^(k-1)*x^k/(1-(3*k/2+1)*x)^(k+1)))
%Y A372235 Cf. A349562, A362694, A362734, A372236.
%K A372235 nonn
%O A372235 0,2
%A A372235 _Seiichi Manyama_, Apr 24 2024