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

Author

Seiichi Manyama, Apr 14 2023

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..417
• Eric Weisstein's World of Mathematics, Lambert W-Function.

Crossrefs

Cf. A000272, A034940, A277614, A362293.

Programs

PARI

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

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).