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Expansion of exp(x*Bernoulli(x)) = 1+sum(n>0, a(n)/(n!)^2*x^n)
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%I #6 Mar 31 2012 10:23:14

%S 1,1,0,-9,0,700,-1800,-188160,2069760,114198336,-3503606400,

%T -114527952000,9096958886400,105465242488320,-34233337027169280,

%U 553613206386240000,171717284043841536000,-10454299523104595558400

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

%F a(n)=n!+(n!)^2*(sum(m=1..n-1, sum(k=1..n-m, (k!*stirling1(m+k,m)*stirling2(n-m,k))/(m+k)!)/(n-m)!)), n>0, a(0)=1.

%o (Maxima)

%o a(n):=(n)!+(n!)^2*(sum(sum((k!*stirling1(m+k,m)*stirling2(n-m,k))/(m+k)!,k,1,n-m)/(n-m)!,m,1,n-1));

%K sign

%O 0,4

%A _Vladimir Kruchinin_, Jun 06 2011