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Expansion of exp(x^2*cos(x))=1+sum(n>0, a(n)*x^(2*n)/(2*n-2)!)
0

%I #8 Mar 31 2012 10:23:13

%S 1,1,0,-7,-31,1961,33479,-2954291,-99285005,13732118161,626849624303,

%T -147178659823339,-6633094420983493,3009425456871930073,

%U 78615467831373410599,-102564663540919291661795,1659425702018862505784819,5254049082422729980286018849,-472557550132644007343975782945,-370056978319441822040661209657819

%N Expansion of exp(x^2*cos(x))=1+sum(n>0, a(n)*x^(2*n)/(2*n-2)!)

%F a(n)=(2*n-2)!*(sum(k=1..n-1, (2^(1-k)*(sum(i=0..floor((k-1)/2), (k-2*i)^(2*(n-k))*binomial(k,i)))*(-1)^(n-k))/(k!*(2*(n-k))!))+1/n!), n>0, a(0)=1.

%o (Maxima)

%o a(n):=(2*n-2)!*(sum((2^(1-k)*(sum((k-2*i)^(2*(n-k))*binomial(k,i),i,0,floor((k-1)/2)))*(-1)^(n-k))/(k!*(2*(n-k))!),k,1,n-1)+1/n!);

%K sign

%O 0,4

%A _Vladimir Kruchinin_, May 29 2011