A025238 a(n) = a(1)*a(n-1) + a(2)*a(n-2) + ...+ a(n-2)*a(2) for n >= 3.

3, 1, 3, 10, 36, 137, 543, 2219, 9285, 39587, 171369, 751236, 3328218, 14878455, 67030785, 304036170, 1387247580, 6363044315, 29323149825, 135700543190, 630375241380, 2938391049395, 13739779184085, 64430797069375, 302934667061301

Offset

1,1

Links

Table of n, a(n) for n=1..25.

Formula

G.f.: (1+3*x-sqrt(1-6*x+5*x^2))/2 - Michael Somos, Jun 08 2000

G.f.: (1+3*x - (1-5*x)*G(0))/(2*x), where G(k)= 1 + 4*x*(4*k+1)/( (4*k+2)*(1-x) - 2*x*(1-x)*(2*k+1)*(4*k+3)/(x*(4*k+3) + (1-x)*(k+1)/G(k+1))); (continued fraction). - Sergei N. Gladkovskii, Jun 25 2013

D-finite with recurrence n*a(n) +3*(-2*n+3)*a(n-1) +5*(n-3)*a(n-2)=0. - R. J. Mathar, Feb 25 2015

Prog

(PARI) a(n)=polcoeff((1+3*x-sqrt(1-6*x+5*x^2+x*O(x^n)))/2, n)

Crossrefs

Essentially same as A002212.

Sequence in context: A067329 A170860 A170845 * A289066 A126970 A204134

Adjacent sequences: A025235 A025236 A025237 * A025239 A025240 A025241

Keyword

nonn

Author

Clark Kimberling

Status

approved