A025240 a(n) = a(1)*a(n-1) + a(2)*a(n-2) + ...+ a(n-2)*a(2) for n >= 3.

3, 2, 6, 22, 90, 394, 1806, 8558, 41586, 206098, 1037718, 5293446, 27297738, 142078746, 745387038, 3937603038, 20927156706, 111818026018, 600318853926, 3236724317174, 17518619320890, 95149655201962, 518431875418926, 2832923350929742

Offset

1,1

Links

Robert Israel, Table of n, a(n) for n = 1..1306

Formula

G.f.: (1+3*x-sqrt(1-6*x+x^2))/2. - Michael Somos, Jun 08 2000

D-finite with recurrence n*a(n) +3*(-2*n+3)*a(n-1) +(n-3)*a(n-2)=0. - R. J. Mathar, Feb 25 2015

Maple

f:= gfun:-rectoproc({n*a(n) +3*(-2*n+3)*a(n-1) +(n-3)*a(n-2)=0, a(1)=3, a(2)=2}, a(n), remember):
map(f, [$1..30]); #  Robert Israel, Sep 28 2025

Mathematica

Rest[CoefficientList[Series[(1+3x-Sqrt[1-6x+x^2])/2, {x, 0, 40}], x]] (* Harvey P. Dale, Aug 26 2013 *)

Prog

(PARI) a(n)=polcoeff((1+3*x-sqrt(1-6*x+x^2+x*O(x^n)))/2, n)

Crossrefs

Essentially same as A006318.

Sequence in context: A140230 A356563 A334588 * A382072 A137602 A086550

Adjacent sequences: A025237 A025238 A025239 * A025241 A025242 A025243

Keyword

nonn

Author

Clark Kimberling

Status

approved