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

0,3

Links

Table of n, a(n) for n=0..17.

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

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).

a(n) ~ -(-1)^n * sqrt(1 + LambertW(-exp(-1)/3)) * n^(n-1) / (3 * (-LambertW(-exp(-1)/3))^n * exp(n + 1/3)). - Vaclav Kotesovec, Jan 30 2026

Prog

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

Crossrefs

Cf. A273954, A360473, A362656, A362671.

Sequence in context: A333385 A331114 A245265 * A143639 A382042 A143412

Adjacent sequences: A362669 A362670 A362671 * A362673 A362674 A362675

Keyword

sign

Author

Seiichi Manyama, Apr 29 2023

Status

approved