A277498 E.g.f.: -LambertW(-sin(x)).

0, 1, 2, 8, 56, 536, 6528, 96592, 1683072, 33760576, 766283264, 19417068032, 543351873536, 16642224306176, 553782090473472, 19893884376859648, 767355755629215744, 31631864049541107712, 1387750771948607504384, 64561526675221208563712

Offset: 0

Author

Vaclav Kotesovec, Oct 18 2016

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..385

Crossrefs

Cf. A238085, A277461, A277475, A277499, A277500.

Programs

Mathematica

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

PARI

x='x+O('x^50); concat([0], Vec(serlaplace(- lambertw(-sin(x))))) \\ G. C. Greubel, Nov 08 2017

Formula

a(n) ~ (1-exp(-2))^(1/4) * (arcsin(exp(-1)))^(1/2-n) * exp(1/2-n) * n^(n-1).