A376145 E.g.f. satisfies A(x) = exp( x * (1+x)^3 * A(x) ).

1, 1, 9, 88, 1265, 23916, 558427, 15608986, 508516017, 18936594712, 793902926771, 37017671474334, 1900666877186761, 106576903636156084, 6481047448001720427, 424870924596413523106, 29871349825140536394593, 2242231079099137007066544

Offset: 0

Author

Seiichi Manyama, Sep 11 2024

Keywords

• nonn

Links

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

Crossrefs

Cf. A362771, A362772, A376146.

Cf. A360076, A367789.

Programs

PARI

my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(-lambertw(-x*(1+x)^3))))

Formula

E.g.f.: exp( -LambertW(-x * (1+x)^3) ).

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