A025228 a(n) = a(1)*a(n-1) + a(2)*a(n-2) + ...+ a(n-1)*a(1) for n >= 3, with initial terms 2,1.

2, 1, 4, 17, 76, 354, 1704, 8421, 42508, 218318, 1137400, 5996938, 31940792, 171605956, 928931280, 5061593709, 27739833228, 152809506582, 845646470616, 4699126915422, 26209721959656, 146681521121244, 823429928805936, 4635568494271458

Offset: 1

Author

Clark Kimberling

Keywords

• nonn

Comments

Essentially A005572 shifted right twice, and 2 prepended.

Links

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

Programs

Mathematica

Rest[CoefficientList[Series[(1-Sqrt[1-8x+12x^2])/2,{x,0,30}],x]]  (* Harvey P. Dale, Apr 20 2011 *)

PARI

a(n)=polcoeff((1-sqrt(1-8*x+12*x^2+x*O(x^n)))/2,n)

Formula

G.f.: (1-sqrt(1-8*x+12*x^2))/2. - Michael Somos, Jun 08 2000

n*a(n) = (8*n-12)*a(n-1) - 12*(n-3)*a(n-2). [Richard Choulet, Dec 16 2009]

a(n) ~ 6^(n-1/2)/(2*sqrt(Pi)*n^(3/2)). - Vaclav Kotesovec, Oct 11 2013

Extensions

Name clarified by Robert C. Lyons, Feb 06 2025