A009756 Expansion of e.g.f. tan(x)/cos(sinh(x)), odd powers only.

1, 5, 81, 2477, 124513, 9330485, 977555697, 136714167389, 24639427576513, 5566295195214053, 1541371979776273041, 513628137925507217549, 202807061788804647209761, 93651309146079155756811029, 50008862201366935181522322225, 30579839563414166184921341412413

Offset

1,2

Links

G. C. Greubel, Table of n, a(n) for n = 1..232

Formula

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

Mathematica

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

Prog

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

Crossrefs

Sequence in context: A278883 A307376 A009733 * A336807 A188419 A009634

Adjacent sequences: A009753 A009754 A009755 * A009757 A009758 A009759

Keyword

nonn

Author

R. H. Hardin

Extensions

Extended and signs tested by Olivier Gérard, Mar 15 1997

Changed offset to 1 by Vaclav Kotesovec, Jan 24 2015

Status

approved