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

0,3

Links

Table of n, a(n) for n=0..21.

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.

Mathematica

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

Prog

(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);

Crossrefs

Sequence in context: A232368 A333924 A173321 * A065747 A363398 A232309

Adjacent sequences: A191495 A191496 A191497 * A191499 A191500 A191501

Keyword

sign

Author

Vladimir Kruchinin, Jun 03 2011

Status

approved