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 A362380 #22 Feb 16 2025 08:34:05
%S A362380 1,1,4,19,154,1456,18136,260002,4430812,85170988,1854422236,
%T A362380 44693165716,1188169271488,34434053438968,1082632555160248,
%U A362380 36666259172292016,1331754793762045456,51622725829298301520,2127683533625205288400
%N A362380 E.g.f. satisfies A(x) = exp(x + 3*x^2/2 * A(x)).
%H A362380 Seiichi Manyama, <a href="/A362380/b362380.txt">Table of n, a(n) for n = 0..392</a>
%H A362380 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LambertW-Function.html">Lambert W-Function</a>.
%F A362380 E.g.f.: exp(x - LambertW(-3*x^2/2 * exp(x))) = -2 * LambertW(-3*x^2/2 * exp(x))/(3*x^2).
%F A362380 a(n) = n! * Sum_{k=0..floor(n/2)} (3/2)^k * (k+1)^(n-k-1) / (k! * (n-2*k)!).
%t A362380 nmax = 20; A[_] = 1;
%t A362380 Do[A[x_] = Exp[x + 3*x^2/2*A[x]] + O[x]^(nmax+1) // Normal, {nmax}];
%t A362380 CoefficientList[A[x], x]*Range[0, nmax]! (* _Jean-François Alcover_, Mar 04 2024 *)
%o A362380 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(x-lambertw(-3*x^2/2*exp(x)))))
%Y A362380 Column k=3 of A362377.
%Y A362380 Cf. A362397.
%K A362380 nonn
%O A362380 0,3
%A A362380 _Seiichi Manyama_, Apr 20 2023