A277503 E.g.f.: -LambertW(-arctan(x)).

0, 1, 2, 7, 48, 469, 5584, 80235, 1367040, 26840841, 595623680, 14752565807, 403579762688, 12084385256605, 393093330282496, 13804177426246995, 520496287836012544, 20973496057176404881, 899452315670554017792, 40903215737685386469847

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. A277502.

Programs

Mathematica

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

PARI

x='x+O('x^50); concat([0], Vec(serlaplace(-lambertw(-atan(x))))) \\ G. C. Greubel, Nov 12 2017

Formula

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