A360545 E.g.f. satisfies A(x) = x * exp( 3*(x + A(x))/2 ).

0, 1, 6, 54, 756, 14580, 358668, 10736712, 378823392, 15395255280, 708217959600, 36380741745744, 2064234271203360, 128214974795177088, 8652900673357097472, 630483717450225530880, 49330027417316557012992, 4124992361928178722764544

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.: A(x) = (-2/3) * LambertW(-3*x/2 * exp(3*x/2)).

a(n) = Sum_{k=1..n} (3*k/2)^(n-1) * binomial(n,k) = 3^(n-1) * A100526(n).

a(n) ~ sqrt(1 + LambertW(exp(-1))) * 3^(n-1) * n^(n-1) / (2^(n-1) * exp(n) * LambertW(exp(-1))^n). - Vaclav Kotesovec, Feb 17 2023

Prog

(PARI) my(N=20, x='x+O('x^N)); concat(0, Vec(serlaplace(-2*lambertw(-3*x/2*exp(3*x/2))/3)))
(PARI) a(n) = sum(k=1, n, (3*k/2)^(n-1)*binomial(n, k));

Crossrefs

Cf. A100526, A216857, A360548.

Cf. A360482, A360544.

Sequence in context: A167571 A366232 A138434 * A217238 A171681 A267837

Adjacent sequences: A360542 A360543 A360544 * A360546 A360547 A360548

Keyword

nonn

Author

Seiichi Manyama, Feb 11 2023

Status

approved