A191498 E.g.f. sqrt(1+2*x*exp(2*x)).

1, 1, 3, 3, -7, 25, 267, -2261, -9231, 284337, -464365, -45533741, 430558185, 8212158409, -201645489381, -1064348170245, 94082272856033, -489731454691487, -45404775138028509, 840156145287526819, 20537314081214613465, -913405900816937424519

Offset: 0

Author

Vladimir Kruchinin, Jun 03 2011

Keywords

• sign

Programs

Mathematica

With[{nn=20},CoefficientList[Series[Sqrt[1+2x Exp[2x]],{x,0,nn}], x] Range[0,nn]!] (* Harvey P. Dale, Oct 03 2011 *)

Maxima

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);

Formula

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.