A385424 Expansion of e.g.f. exp( -LambertW(-arcsin(x)) ).

1, 1, 3, 17, 137, 1465, 19499, 311873, 5829073, 124796081, 3012319315, 80960234577, 2398138520409, 77630951407529, 2726829925494011, 103300796618253825, 4198494172961579169, 182239547736082960737, 8414068749731088539299, 411754575622058760824593

Offset

0,3

Links

Table of n, a(n) for n=0..19.

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

Formula

E.g.f. A(x) satisfies A(x) = exp( arcsin(x) * A(x) ).

a(n) = Sum_{k=0..n} (k+1)^(k-1) * A385343(n,k).

a(n) ~ n^(n-1) / (sqrt(cos(exp(-1))) * sin(exp(-1))^(n - 1/2) * exp(n - 3/2)). - Vaclav Kotesovec, Jun 28 2025

Prog

(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(-lambertw(-asin(x)))))

Crossrefs

Cf. A385426, A385427.

Cf. A277502, A381142, A385343, A385425.

Sequence in context: A286896 A244432 A219503 * A230387 A370767 A361626

Adjacent sequences: A385421 A385422 A385423 * A385425 A385426 A385427

Keyword

nonn

Author

Seiichi Manyama, Jun 28 2025

Status

approved