A009750 Expansion of e.g.f. tan(x)*tan(tan(x)), even powers only.

0, 2, 24, 688, 36992, 3234304, 418499584, 75077748736, 17816420974592, 5399699170000896, 2034070241589854208, 932012713402719797248, 510363278595553899839488, 329128604050609873851777024, 246881504912875480553409740800, 213119748914997017969817425018880

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..224

Formula

a(n) ~ (2*n)! * 4 * Pi / ((4+Pi^2) * arctan(Pi/2)^(2*n+1)). - Vaclav Kotesovec, Jan 24 2015

Mathematica

nn = 20; Table[(CoefficientList[Series[Tan[x]*Tan[Tan[x]], {x, 0, 2*nn}], x] * Range[0, 2*nn]!)[[n]], {n, 1, 2*nn+1, 2}] (* Vaclav Kotesovec, Jan 24 2015 *)

Prog

(PARI) x='x+O('x^50); v=Vec(serlaplace(tan(x)*tan(tan(x)))); concat([0], vector(#v\2, n, v[2*n-1])) \\ G. C. Greubel, Feb 12 2018

Crossrefs

Sequence in context: A012375 A012750 A174997 * A030438 A012723 A354335

Adjacent sequences: A009747 A009748 A009749 * A009751 A009752 A009753

Keyword

nonn

Author

R. H. Hardin

Extensions

Extended and signs tested by Olivier Gérard, Mar 15 1997

Status

approved