A362672 E.g.f. satisfies A(x) = exp( x * exp(x) / A(x)^3 ).

1, 1, -3, 37, -679, 17161, -553451, 21731053, -1006118863, 53671172113, -3241671266899, 218677223408821, -16296163119155063, 1329568681331536153, -117874745761237043515, 11283758432396431997821, -1159952212029532257663391, 127445385808282289840496673

Offset: 0

Author

Seiichi Manyama, Apr 29 2023

Keywords

• sign

Links

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

Crossrefs

Cf. A273954, A360473, A362656, A362671.

Programs

PARI

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

Formula

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

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