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%I #20 Jul 26 2018 03:43:03
%S 1,-1,13,-301,11705,-698521,59340997,-6782462597,1000434618609,
%T -184576848771889,41577074746699261,-11216502744649033437,
%U 3567416307426404300713,-1320192785381894987925961,562163981454375064332029365,-272809563505907130928868599861
%N Expansion of e.g.f. cos(x/cosh(x)) (even powers only).
%H G. C. Greubel, <a href="/A009119/b009119.txt">Table of n, a(n) for n = 0..238</a>
%F a(n) = 2*Sum_{k=1..n-1} binomial(2*n,2*k)*Sum_{j=0..(n-k)} binomial(k+j-1,j)*4^(n-k-j)*Sum_{i=0..j} (i-j)^(2*n-2*k)*binomial(2*j,i)*(-1)^(k+j-i) +(-1)^n. - _Vladimir Kruchinin_, Jun 16 2011
%t With[{nn=30},Take[CoefficientList[Series[Cos[x/Cosh[x]],{x,0,nn}],x] Range[ 0,nn]!,{1,-1,2}]] (* _Harvey P. Dale_, Jul 07 2017 *)
%o (Maxima)
%o a(n):=2*sum(binomial(2*n,2*k)*sum(binomial(k+j-1,j)*4^(n-k-j)*sum((i-j)^(2*n-2*k)*binomial(2*j,i)*(-1)^(k+j-i),i,0,j),j,0,(n-k)),k,1,n-1)+(-1)^n; /* _Vladimir Kruchinin_, Jun 16 2011 */
%o (PARI) x='x+O('x^50); v=Vec(serlaplace(cos(x/cosh(x)))); vector(#v\2,n,v[2*n-1]) \\ _G. C. Greubel_, Jul 26 2018
%K sign
%O 0,3
%A _R. H. Hardin_
%E Extended with signs by _Olivier Gérard_, Mar 15 1997
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