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%I #8 Mar 19 2018 15:25:21
%S 1,0,6,15,1596,28155,2752266,152499165,18328556616,2081907926295,
%T 342948671262246,63036450590713545,14410958655520684956,
%U 3796531150529363706915,1173277778862573074248746,415134737359852340707539405,167697531024902643857808300816,76517905142019788108453415876015
%N E.g.f. (even powers only) cos(x)^(cos(x)-1)
%F a(n)=2*sum(k=1..2*n, sum(r=0..2*n-k, (stirling1(r,k)*sum(j=1..r+k, ((sum(i=0..(j-1)/2, (j-2*i)^(2*n)*binomial(j,i)))*(-1)^(r+k+n-j)*binomial(r+k,j))/2^j))/(r)!)), n>0, a(0)=1.
%t With[{nn=40},Take[CoefficientList[Series[Cos[x]^(Cos[x]-1),{x,0,nn}],x] Range[0,nn]!,{1,-1,2}]] (* _Harvey P. Dale_, Mar 19 2018 *)
%o (Maxima)
%o a(n):=2*sum(sum((stirling1(r,k)*sum(((sum((j-2*i)^(2*n)*binomial(j,i),i,0,(j-1)/2))*(-1)^(r+k+n-j)*binomial(r+k,j))/2^j,j,1,r+k))/(r)!,r,0,2*n-k),k,1,2*n);
%K nonn
%O 0,3
%A _Vladimir Kruchinin_, Jun 03 2011