A025232 a(n) = a(1)*a(n-1) + a(2)*a(n-2) + ...+ a(n-1)*a(1) for n >= 3, with initial terms 3,2.

3, 2, 12, 76, 504, 3472, 24672, 179792, 1337376, 10117312, 77618304, 602528640, 4724294400, 37361809920, 297683352576, 2387325283584, 19255919325696, 156110855965696, 1271401468151808

Offset: 1

Author

Clark Kimberling

Keywords

• nonn

Links

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

Programs

Mathematica

Rest[CoefficientList[Series[(1-Sqrt[1-12*x+28*x^2])/2, {x, 0, 20}], x]] (* Vaclav Kotesovec, Oct 11 2013 *)
nxt[{n_,a_,b_,c_}]:={n+1,b,c,(c(12n-6)-28(n-2)*b)/(n+1)}; NestList[ nxt,{3,3,2,12},20][[All,2]] (* Harvey P. Dale, Jun 04 2019 *)

PARI

a(n)=polcoeff((1-sqrt(1-12*x+28*x^2+x*O(x^n)))/2,n)

Formula

G.f.: (1-sqrt(1-12*x+28*x^2))/2. - Michael Somos, Jun 08 2000

n*a(n) = (12*n-18)*a(n-1)-28*(n-3)*a(n-2). - Richard Choulet, Dec 16 2009

a(n) ~ sqrt(3*sqrt(2)-2) * (2*(3+sqrt(2)))^n / (2*sqrt(14*Pi)*n^(3/2)). - Vaclav Kotesovec, Oct 11 2013

Extensions

Name clarified by Robert C. Lyons, Feb 06 2025