A362655 E.g.f. satisfies A(x) = exp( x * exp(x^3) * A(x) ).

1, 1, 3, 16, 149, 1656, 22567, 369664, 7081209, 155178928, 3830958251, 105267080304, 3187172910517, 105437661606616, 3784329536385231, 146474021771040856, 6081955388047685873, 269686446704697314016, 12719466142269818201299

Offset: 0

Author

Seiichi Manyama, Apr 28 2023

Keywords

• nonn

Links

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

Crossrefs

Cf. A273954, A362654.

Cf. A354553, A362674.

Programs

PARI

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

Formula

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

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