A025239 a(n) = a(1)*a(n-1) + a(2)*a(n-2) + ...+ a(n-2)*a(2) for n >= 3.

2, 3, 6, 21, 78, 318, 1356, 5997, 27222, 126138, 594132, 2836290, 13692300, 66729180, 327855768, 1622216829, 8076311142, 40427919714, 203353800324, 1027318915254, 5210182030308, 26517609163812, 135397544040744, 693364054299474

Offset: 1

Author

Clark Kimberling

Keywords

• nonn

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..200

Crossrefs

Essentially the same as A025229.

Programs

Mathematica

Join[{2},Drop[CoefficientList[Series[(1-Sqrt[1-4x-8x^2])/2, {x,0,30}], x],2]] (* Harvey P. Dale, Nov 05 2011 *)

PARI

a(n)=polcoeff((1-sqrt(1-4*x-8*x^2+x*O(x^n)))/2,n)

Formula

G.f.: (1-sqrt(1-4*x-8*x^2))/2. - Michael Somos, Jun 08 2000

Recurrence (for n>3): n*a(n) = 2*(2*n-3)*a(n-1) + 8*(n-3)*a(n-2). - Vaclav Kotesovec, Oct 07 2012

a(n) ~ sqrt(3-sqrt(3))*(2+2*sqrt(3))^n/(4*sqrt(Pi)*n^(3/2)). - Vaclav Kotesovec, Oct 07 2012