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%I #17 Jul 28 2018 16:23:45
%S 1,1,0,-3,-6,15,75,84,-1820,-123,-10725,475816,-3554562,32763107,
%T -501958275,6877337128,-95130710792,1486984480729,-24736452203529,
%U 430314112493264,-7930867848273070,154362838472661367,-3154456665148212743
%N E.g.f. exp(log(1+x)*cos(x)).
%F a(n)=sum(k=0..n, (sum(m=1..(n-k)/2, binomial(n,2*m)*(stirling1(n-2*m,k)*(sum(i=0..(k-1)/2, (k-2*i)^(2*m)*binomial(k,i)))*(-1)^(m))))/2^(k-1)+(stirling1(n,k))). - _Vladimir Kruchinin_, Jun 29 2011
%F E.g.f.: (1+x)^cos(x). - _Vaclav Kotesovec_, Jul 28 2018
%F a(n) ~ (-1)^n * n! / (Gamma(-cos(1)) * n^(1 + cos(1))). - _Vaclav Kotesovec_, Jul 28 2018
%o (Maxima)
%o a(n):=sum((sum(binomial(n,2*m)*(stirling1(n-2*m,k)*(sum((k-2*i)^(2*m)*binomial(k,i),i,0,(k-1)/2))*(-1)^(m)),m,1,(n-k)/2))/2^(k-1)+(stirling1(n,k)),k,0,n); /* _Vladimir Kruchinin_, Jun 29 2011 */
%K sign,easy
%O 0,4
%A _R. H. Hardin_
%E Extended with signs by _Olivier Gérard_, Mar 15 1997
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