A376516 - OEIS

%I #12 Feb 16 2025 08:34:07

%S 1,0,0,6,24,120,1800,20160,221760,3507840,59875200,1037836800,

%T 20776694400,459761702400,10686605529600,268901439206400,

%U 7318617546240000,210804082384896000,6440850193262284800,209115023566972723200,7157303732396353536000,257535328655939862528000

%N E.g.f. satisfies A(x) = exp(x^3 * A(x) / (1 - x)).

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LambertW-Function.html">Lambert W-Function</a>.

%F E.g.f.: exp( -LambertW(-x^3 / (1-x)) ).

%F a(n) = n! * Sum_{k=0..floor(n/3)} (k+1)^(k-1) * binomial(n-2*k-1,n-3*k)/k!.

%o (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(-lambertw(-x^3/(1-x)))))

%o (PARI) a(n) = n!*sum(k=0, n\3, (k+1)^(k-1)*binomial(n-2*k-1, n-3*k)/k!);

%Y Cf. A052868, A376515.

%Y Cf. A376495.

%K nonn,easy

%O 0,4

%A _Seiichi Manyama_, Sep 26 2024