A009761 Expansion of e.g.f. tan(x)/cosh(sin(x)), odd powers only.

1, -1, 41, -673, 45457, -2687521, 313663481, -40066499905, 7520482865953, -1641264931094209, 461539011599816393, -151789031893211252065, 60285747097883123598001, -27699643878162362856467425, 14824242336112602473956467353, -9047638464118811277582522202369

Offset

1,3

Links

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

Formula

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

Mathematica

nn = 20; Table[(CoefficientList[Series[Sech[Sin[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)/cosh(sin(x)))); vector((#v-1)\2 , n, v[2*n-1]) \\ G. C. Greubel, Feb 12 2018

Crossrefs

Sequence in context: A268748 A143010 A009730 * A118448 A298459 A163039

Adjacent sequences: A009758 A009759 A009760 * A009762 A009763 A009764

Keyword

sign

Author

R. H. Hardin

Extensions

Extended with signs by Olivier Gérard, Mar 15 1997

Changed offset to 1 by Vaclav Kotesovec, Jan 24 2015

Status

approved