A277498 -id:A277498

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A277500

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

+10
3

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,3

LINKS

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

FORMULA

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

MAPLE

S:= series(-LambertW(-tan(x)), x, 31):

seq(coeff(S, x, n)*n!, n=0..30); # Robert Israel, Mar 09 2017

MATHEMATICA

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

PROG

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

CROSSREFS

Cf. A277479, A277467, A277498, A277501.

KEYWORD

nonn

AUTHOR

Vaclav Kotesovec, Oct 18 2016

STATUS

approved

A277499

E.g.f.: -sin(LambertW(-x)).

+10
2

0, 1, 2, 8, 52, 476, 5646, 82368, 1426888, 28623376, 652516090, 16660233600, 470930272572, 14598765522368, 492441140292934, 17955574113204224, 703714660937658128, 29500170665998713088, 1317136516654501334898, 62399954043306802391040

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,3

LINKS

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

FORMULA

a(n) ~ cos(1) * n^(n-1).

MAPLE

S:= series(-sin(LambertW(-x)), x, 31):

seq(coeff(S, x, n)*n!, n=0..30); # Robert Israel, Oct 30 2016