A371039 E.g.f. satisfies A(x) = exp(x^3*A(x)) / (1-x).

1, 1, 2, 12, 72, 480, 4680, 52920, 645120, 9313920, 153014400, 2720995200, 53428636800, 1154333980800, 26847281260800, 671610658118400, 18064388076134400, 517898679679180800, 15763026427487539200, 508612525689235968000, 17329554246181072896000

Offset: 0

Author

Seiichi Manyama, Mar 09 2024

Keywords

• nonn

Links

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

Crossrefs

Cf. A352410, A371038.

Programs

PARI

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

PARI

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

Formula

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

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