A012725 Expansion of e.g.f. exp(arctanh(x)*tan(x)) (even powers only).

1, 2, 28, 920, 54416, 5056288, 678865856, 124425704832, 29873423298816, 9104340085891584, 3435702339713424384, 1573394503700675106816, 859935938676055185002496, 553085284375423405752918016

Offset

0,2

Links

Robert Israel, Table of n, a(n) for n = 0..225

Formula

a(n) ~ 2 * (2*n-1)! * (4*n)^(tan(1)/2) / GAMMA(tan(1)/2). - Vaclav Kotesovec, Oct 24 2013

Example

1 + (2/2!)*x^2 + (28/4!)*x^4 + (920/6!)*x^6 + (54416/8!)*x^8 + ...

Maple

S:= series(exp(arctanh(x)*tan(x)), x, 31):
seq(coeff(S, x, j)*j!, j=0..30, 2); # Robert Israel, Aug 07 2023

Mathematica

With[{nn=30}, Take[CoefficientList[Series[Exp[ArcTanh[x]Tan[x]], {x, 0, nn}], x] Range[0, nn]!, {1, -1, 2}]] (* Harvey P. Dale, Mar 25 2013 *)

Crossrefs

Sequence in context: A264411 A370378 A009256 * A264637 A352251 A012756

Adjacent sequences: A012722 A012723 A012724 * A012726 A012727 A012728

Keyword

nonn

Author

Patrick Demichel (patrick.demichel(AT)hp.com)

Status

approved