A371040 E.g.f. satisfies A(x) = exp(x^3*A(x)^2) / (1-x).

1, 1, 2, 12, 96, 840, 9720, 143640, 2399040, 45239040, 976752000, 23537606400, 621444700800, 17936155036800, 562855739846400, 19038932398886400, 690456599575142400, 26748823900403404800, 1102407824344284057600, 48147134965603914240000

Offset: 0

Author

Seiichi Manyama, Mar 09 2024

Keywords

• nonn

Links

• Eric Weisstein's World of Mathematics, Lambert W-Function.

Crossrefs

Cf. A360601, A370875.

Programs

PARI

my(N=30, x='x+O('x^N)); Vec(serlaplace(sqrt(lambertw(-2*x^3/(1-x)^2)/(-2*x^3))))

PARI

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

Formula

E.g.f.: sqrt(LambertW( -2*x^3/(1-x)^2 ) / (-2*x^3)).

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