A012303 Expansion of e.g.f. sech(sin(x)*sin(x)), even powers only.

1, 0, -12, 240, 4368, -942720, 42639168, 8638506240, -2287049555712, 38746394603520, 145600412857955328, -42974022434701332480, -7760313189299657306112, 11863589839842518338928640

Offset

0,3

Links

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

Example

E.g.f. = 1 - 12*x^4/4! + 240*x^6/6! + 4368*x^8/8! + ...

Maple

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

Mathematica

With[{nn = 100}, CoefficientList[Series[Sech[Sin[x]^2], {x, 0, nn}], x] Range[0, nn]!][[1 ;; ;; 2]] (* G. C. Greubel, Oct 25 2018 *)

Prog

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

Crossrefs

Sequence in context: A012544 A009052 A213449 * A119837 A012538 A006588

Adjacent sequences: A012300 A012301 A012302 * A012304 A012305 A012306

Keyword

sign

Author

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

Status

approved