A144575 E,g.f.: exp(1-sqrt(1-2*x-3*x^2)).

1, 1, 5, 25, 217, 2321, 32221, 536425, 10547825, 238451617, 6103391221, 174418724921, 5506024371145, 190282381973425, 7145586497798477, 289733147423281801, 12615792602988127201, 587128127734854278465, 29084008051746449028325, 1527881758843209566647897

Offset: 0

Author

N. J. A. Sloane, Jan 07 2009

Keywords

• nonn

Crossrefs

Cf. A001515, A144576.

Programs

Mathematica

With[{nn=20},CoefficientList[Series[Exp[1-Sqrt[1-2x-3x^2]],{x,0,nn}],x] Range[ 0,nn]!] (* Harvey P. Dale, Mar 26 2013 *)

Formula

a(n) ~ 3^(n-1/2)*sqrt(2)*n^(n-1)/exp(n-1). - Vaclav Kotesovec, Jun 02 2013

Conjecture D-finite with recurrence: a(n) +(-2*n+3)*a(n-1) +(-3*n^2+12*n-10)*a(n-2) +3*(-2*n+3)*a(n-3) -9*(n-1)*(n-3)*a(n-4)=0. - R. J. Mathar, Jan 24 2020