A009558 - OEIS

%I #29 Jan 22 2018 02:38:44

%S 1,-4,56,-1576,74944,-5428864,556999808,-76901598208,13750425100288,

%T -3091282934198272,853453694386847744,-283870980665283248128,

%U 111959859759125683142656,-51664166661084786641993728

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

%H Vincenzo Librandi, <a href="/A009558/b009558.txt">Table of n, a(n) for n = 1..100</a>

%F 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

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

%t 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 *)

%o (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

%K sign

%O 1,2

%A _R. H. Hardin_

%E Extended with signs by _Olivier Gérard_, Mar 15 1997

%E Definition clarified by _Harvey P. Dale_, May 16 2012