A377374 Expansion of e.g.f. (1/x) * Series_Reversion( x / (exp(-x) + 3*x) ).

1, 2, 9, 65, 653, 8439, 133609, 2506727, 54408633, 1341637595, 37055451101, 1133391705819, 38034022035877, 1389484163236727, 54899323023464529, 2332723285215012479, 106076669681270501105, 5140202768545661266227, 264427503283923495485221, 14392750805365239040586051

Offset: 0

Author

Seiichi Manyama, Dec 28 2024

Keywords

• nonn

Links

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

Crossrefs

Cf. A108919, A377373.

Cf. A376107.

Programs

PARI

my(N=30, x='x+O('x^N)); Vec(serlaplace(lambertw(x/(1-3*x))/x))

PARI

a(n) = n!*sum(k=0, n, (-1)^k*3^(n-k)*(k+1)^(k-1)*binomial(n, k)/k!);

Formula

E.g.f.: (1/x) * LambertW(x / (1 - 3*x)).

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

a(n) = A376107(n+1)/(n+1).