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 A378095 #12 Feb 16 2025 08:34:07
%S A378095 1,1,2,12,120,1320,16200,234360,3991680,77535360,1678924800,
%T A378095 40142995200,1053264643200,30109980700800,931249403884800,
%U A378095 30979797430982400,1103292884684390400,41889177988142284800,1689202127352118579200,72105273328152166502400
%N A378095 E.g.f. satisfies A(x) = exp( x^3 * A(x) / (1-x)^2 ) / (1-x).
%H A378095 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LambertW-Function.html">Lambert W-Function</a>.
%F A378095 E.g.f.: exp( -LambertW(-x^3/(1-x)^3) )/(1-x).
%F A378095 a(n) = n! * Sum_{k=0..floor(n/3)} (k+1)^(k-1) * binomial(n,3*k)/k!.
%o A378095 (PARI) a(n) = n!*sum(k=0, n\3, (k+1)^(k-1)*binomial(n, 3*k)/k!);
%Y A378095 Cf. A352410, A378094.
%K A378095 nonn
%O A378095 0,3
%A A378095 _Seiichi Manyama_, Nov 16 2024