A277479 -id:A277479 - cp's OEIS frontend

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

Vaclav Kotesovec, Oct 17 2016

nonn

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

Cf. A000169, A277468, A277473, A277479.

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

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

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

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

A277500 E.g.f.: -LambertW(-tan(x)).

Original entry on oeis.org

0, 1, 2, 11, 80, 821, 10608, 167215, 3105024, 66433129, 1609025024, 43521156755, 1300287942656, 42528924900125, 1511407185512448, 57992816331075511, 2389444376908726272, 105219795048784564945, 4931495123285481881600, 245105773365008603770907

Offset: 0

Vaclav Kotesovec, Oct 18 2016

nonn

Robert Israel, Table of n, a(n) for n = 0..384

Cf. A277479, A277467, A277498, A277501.

S:= series(-LambertW(-tan(x)),x,31):
seq(coeff(S,x,n)*n!,n=0..30); # Robert Israel, Mar 09 2017

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

x='x+O('x^50); concat([0], Vec(serlaplace(-lambertw(-tan(x))))) \\ G. C. Greubel, Nov 07 2017

a(n) ~ sqrt(1+exp(-2)) * arctan(exp(-1))^(1/2-n) * exp(1/2-n) * n^(n-1).

cp's OEIS Frontend

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

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