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%I #14 May 08 2014 06:37:22
%S 1,1,3,3,-7,25,267,-2261,-9231,284337,-464365,-45533741,430558185,
%T 8212158409,-201645489381,-1064348170245,94082272856033,
%U -489731454691487,-45404775138028509,840156145287526819,20537314081214613465,-913405900816937424519
%N E.g.f. sqrt(1+2*x*exp(2*x)).
%F a(n) = n!*sum(k=1..n, (k^(n-k-1)*(-1)^(k+1)*C(2*k-2,k-1)*2^(n-2*k+1))/(n-k)!), n>0, a(0)=1.
%t With[{nn=20},CoefficientList[Series[Sqrt[1+2x Exp[2x]],{x,0,nn}], x] Range[0,nn]!] (* _Harvey P. Dale_, Oct 03 2011 *)
%o (Maxima)
%o a(n):= n!*sum((k^(n-k-1)*(-1)^(k+1)*binomial(2*k-2,k-1)*2^(n-2*k+1))/(n-k)!, k,1,n);
%K sign
%O 0,3
%A _Vladimir Kruchinin_, Jun 03 2011
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