A009558 Expansion of e.g.f. sin(x)/cosh(sin(x)) (odd powers only).

1, -4, 56, -1576, 74944, -5428864, 556999808, -76901598208, 13750425100288, -3091282934198272, 853453694386847744, -283870980665283248128, 111959859759125683142656, -51664166661084786641993728

Offset

1,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..100

Formula

a(n) ~ (-1)^(n+1) * 2*Pi* (2*n-1)! / (sqrt(4+Pi^2) * log(Pi/2 + sqrt(1+Pi^2/4))^(2*n)). - Vaclav Kotesovec, Apr 20 2014

Example

sin(x)/cosh(sin(x)) = 1*x/1! - 4*x^3/3! + 56*x^5/5! - 1576*x^7/7! + ...

Mathematica

With[{nn=30}, Take[CoefficientList[Series[Sin[x]/Cosh[Sin[x]], {x, 0, nn}], x]Range[0, nn-1]!, {2, -1, 2}]] (* Harvey P. Dale, May 16 2012 *)

Prog

(PARI) x='x+O('x^50); v=Vec(serlaplace(sin(x)/cosh(sin(x)))); vector((#v-1)\2 , n, v[2*n-1]) \\ G. C. Greubel, Jan 21 2018

Crossrefs

Sequence in context: A377429 A277038 A009536 * A113583 A174489 A009563

Adjacent sequences: A009555 A009556 A009557 * A009559 A009560 A009561

Keyword

sign

Author

R. H. Hardin

Extensions

Extended with signs by Olivier Gérard, Mar 15 1997

Definition clarified by Harvey P. Dale, May 16 2012

Status

approved