A362283 Expansion of e.g.f. exp( sqrt(-LambertW(-x^2)) ).

1, 1, 1, 4, 13, 106, 601, 7456, 60649, 1012348, 10748161, 225641296, 2957978101, 74847384184, 1168123938073, 34598428916416, 626497273410961, 21261683280971536, 438222313050326209, 16765636110497697088, 387549609831150094621, 16502188154766906299296

Offset

0,4

Links

Seiichi Manyama, Table of n, a(n) for n = 0..417

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

Formula

a(0) = 1; a(n) = Sum_{k=0..floor((n-1)/2)} A034940(k) * binomial(n-1,2*k) * a(n-2*k-1).

a(n) ~ (1 - (-1)^n/exp(2)) * n^(n-1) / (sqrt(2) * exp(n/2 - 1)). - Vaclav Kotesovec, Jan 30 2026

Prog

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

Crossrefs

Cf. A000272, A034940, A277614, A362293.

Sequence in context: A290392 A261785 A331013 * A276912 A045886 A015460

Adjacent sequences: A362280 A362281 A362282 * A362284 A362285 A362286

Keyword

nonn

Author

Seiichi Manyama, Apr 14 2023

Status

approved