%I #12 Jan 31 2018 03:40:40
%S 0,1,1,16,211,3151,73096,2222221,78804181,3328776376,168350871991,
%T 9890935452091,660814861059376,49911348691790041,4239141233825894761,
%U 401191146623474166976,41953203382631444827771,4820014734080867077534471
%N Expansion of e.g.f. sinh(cosh(x)-1), (even terms only).
%D L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 226, 7th line of table.
%H G. C. Greubel, <a href="/A059385/b059385.txt">Table of n, a(n) for n = 0..250</a>
%F a(n) = b(2*n) where b(n) = ((-1)^n+1)/4*Sum(k=1..n/2, ((Sum(j=1..k,((Sum(i=0..j,(j-2*i)^n*binomial(j,i)))*(-1)^(k-j)*binomial(k,j) )/2^(j)))*(1-(-1)^k)/(k!))). - _Vladimir Kruchinin_, Apr 23 2011
%t With[{nn = 50}, CoefficientList[Series[Sinh[Cosh[x] - 1], {x, 0, nn}], x] Range[0, nn]!][[1 ;; ;; 2]] (* _G. C. Greubel_, Jan 29 2018 *)
%o (Maxima)
%o a(n):=b(2*n);
%o b(n):=((-1)^n+1)/4*sum(((sum(((sum((j-2*i)^n*binomial(j,i),i,0,j))*(-1)^(k-j)*binomial(k,j))/2^(j),j,1,k))*(1-(-1)^k)/(k!)),k,1,n/2);
%o /* _Vladimir Kruchinin_, Apr 23 2011 */
%o (PARI) x='x+O('x^50); v=Vec(serlaplace(sinh(cosh(x)-1))); concat([0], vector(#v\2,n,v[2*n-1])) \\ _G. C. Greubel_, Jan 29 2018
%K nonn
%O 0,4
%A _N. J. A. Sloane_, Jan 28 2001