A340474 a(n) = n! [x^n] LW(T(x)), where T(x) = -W(-x) Euler's tree function, W(x) is the Lambert W function, and LW(x) = W(-W(x))/(-W(x)) (A340473).

1, 1, 3, 22, 209, 2756, 43717, 839686, 18581425, 470707192, 13352676101, 420875581754, 14566375690297, 549877190829604, 22472783629465093, 989043215802778966, 46631075599107558113, 2345376059569552767344, 125350843842721213505029, 7095169059445749303612946

Offset: 0

Author

Peter Luschny, Jan 09 2021

Keywords

• nonn

Crossrefs

Cf. A340473, A097174, A177885, A207833, A227176.

Cf. A000169, A000272.

Programs

Maple

W := x -> LambertW(x): T := x -> -W(-x): LW := x -> W(-W(x))/(-W(x)):
ser := series(LW(T(x)), x, 24): seq(n!*coeff(ser, x, n), n=0..19);