A277480 E.g.f.: -tanh(x)*LambertW(-x).

0, 0, 2, 6, 28, 280, 3486, 50624, 877080, 17677440, 404537050, 10360548352, 293676213876, 9126971869184, 308568877413174, 11274243944693760, 442681525701106096, 18588860836606935040, 831243363178769061426, 39436124829328468606976, 1978382154057910059275340

Offset: 0

Author

Vaclav Kotesovec, Oct 17 2016

Keywords

• nonn

Links

• Robert Israel, Table of n, a(n) for n = 0..387

Crossrefs

Cf. A000169, A277468, A277473, A277479.

Programs

Maple

F:= proc(m) option remember; add(binomial(m,2*k+1)*(m-2*k-1)^(m-2*k-2),k=0..floor(m/2)-1) - add(binomial(m,2*k)*procname(m-2*k),k=1..floor(m/2)) end proc:
map(F, [$0..30]); # Robert Israel, Oct 26 2016

Mathematica

CoefficientList[Series[-Tanh[x]*LambertW[-x], {x, 0, 20}], x] * Range[0, 20]!

PARI

x='x+O('x^50); concat([0,0],Vec(serlaplace(tanh(-x)*lambertw(-x))) ) \\ G. C. Greubel, Nov 05 2017

Formula

a(n) ~ tanh(exp(-1)) * n^(n-1).

a(n) = Sum_{k=0..floor(n/2)-1} binomial(n,2*k+1)*(m-2*k-1)^(m-2*k-2) - Sum_{k=1..floor(n/2)} binomial(n,2*k)*a(n-2*k). - Robert Israel, Oct 26 2016