A025228 - OEIS

A025228

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

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

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OFFSET

1,1

COMMENTS

Essentially A005572 shifted right twice, and 2 prepended.

LINKS

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

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

MATHEMATICA

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

PROG

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

CROSSREFS

Sequence in context: A346793 A087801 A238454 * A267377 A132945 A192494

Adjacent sequences: A025225 A025226 A025227 * A025229 A025230 A025231

KEYWORD

nonn

AUTHOR

Clark Kimberling

STATUS

approved