A012302 Expansion of e.g.f. sec(sin(x)*sin(x)), even powers only.

1, 0, 12, -240, 12432, -1073280, 125898432, -20938794240, 4567638266112, -1267670125547520, 437480763704527872, -183445824359628779520, 91908363767795383898112, -54223577318067990113648640

Offset

0,3

Links

G. C. Greubel, Table of n, a(n) for n = 0..225

Formula

a(n) ~ 2 * (-1)^n * (2*n)! / (sqrt(Pi*(2+Pi)) * (log(sqrt(Pi/2) + sqrt(1+Pi/2)))^(2*n+1)). - Vaclav Kotesovec, Feb 08 2015

Example

sec(sin(x)*sin(x)) = 1 + 12/4!*x^4 - 240/6!*x^6 + 12432/8!*x^8 + ...

Maple

seq(coeff(series(factorial(n)*sec(sin(x)*sin(x)), x, n+1), x, n), n = 0 .. 26, 2); # Muniru A Asiru, Oct 26 2018

Mathematica

nn = 20; Table[(CoefficientList[Series[Sec[Sin[x]^2], {x, 0, 2*nn}], x] * Range[0, 2*nn]!)[[n]], {n, 1, 2*nn+1, 2}] (* Vaclav Kotesovec, Feb 08 2015 *)

Prog

(PARI) x='x+O('x^50); v=Vec(serlaplace(1/cos(sin(x)*sin(x)))); vector(#v\2, n, v[2*n-1]) \\ G. C. Greubel, Apr 11 2017
(Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!( 1/Cos(Sin(x)^2) ));  [Factorial(2*n)*b[2*n+1]: n in [0..Floor((m-2)/2)]]; // G. C. Greubel, Oct 25 2018

Crossrefs

Cf. A024264.

Sequence in context: A009166 A174556 A012349 * A012543 A012350 A220216

Adjacent sequences: A012299 A012300 A012301 * A012303 A012304 A012305

Keyword

sign

Author

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

Status

approved