A360433 E.g.f. satisfies A(x) = x * exp(A(x) + x^3).

0, 1, 2, 9, 88, 865, 11016, 173929, 3227792, 69010785, 1670970160, 45198840841, 1350754588008, 44196732194641, 1571453132115608, 60331412278617705, 2487385479819549856, 109608035124514365121, 5140910415583354887648, 255708987797133857518345

Offset

0,3

Links

Table of n, a(n) for n=0..19.

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

Formula

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

a(n) ~ sqrt(1+LambertW(3*exp(-3))) * 3^(n/3) * n^(n-1) / (exp(n) * (LambertW(3*exp(-3)))^(n/3)). - Vaclav Kotesovec, Feb 07 2023

Prog

(PARI) my(N=20, x='x+O('x^N)); concat(0, Vec(serlaplace(-lambertw(-x*exp(x^3)))))

Crossrefs

Cf. A216857, A360432.

Cf. A052322.

Sequence in context: A106163 A368186 A359903 * A278332 A135747 A270862

Adjacent sequences: A360430 A360431 A360432 * A360434 A360435 A360436

Keyword

nonn

Author

Seiichi Manyama, Feb 07 2023

Status

approved