A362572 E.g.f. satisfies A(x) = exp(x * A(x)^(x/2)).

1, 1, 1, 4, 13, 76, 421, 3361, 26209, 267688, 2689201, 33579811, 412800961, 6103089994, 88754687113, 1517513934301, 25487131948321, 495009722435176, 9430633148123809, 205154208873930763, 4371962638221712801, 105330237499426955926

Offset

0,4

Links

Seiichi Manyama, Table of n, a(n) for n = 0..439

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

Formula

E.g.f.: (-2 * LambertW(-x^2/2) / x^2)^(2/x) = exp(-2 * LambertW(-x^2/2) / x) = exp(x * exp(-LambertW(-x^2/2))).

a(n) = n! * Sum_{k=0..floor(n/2)} ((n-k)/2)^k * binomial(n-k-1,k)/(n-k)!.

E.g.f.: Sum_{k>=0} (k*x/2 + 1)^(k-1) * x^k / k!.

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x*exp(-lambertw(-x^2/2)))))

Crossrefs

Cf. A000272, A362573.

Cf. A361777.

Sequence in context: A235385 A144055 A012150 * A012261 A012075 A197942

Adjacent sequences: A362569 A362570 A362571 * A362573 A362574 A362575

Keyword

nonn

Author

Seiichi Manyama, Apr 25 2023

Status

approved