A025232 - OEIS

%I #21 Jun 15 2022 11:07:50

%S 3,2,12,76,504,3472,24672,179792,1337376,10117312,77618304,602528640,

%T 4724294400,37361809920,297683352576,2387325283584,19255919325696,

%U 156110855965696,1271401468151808

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

%H Vincenzo Librandi, <a href="/A025232/b025232.txt">Table of n, a(n) for n = 1..200</a>

%F G.f.: (1-sqrt(1-12*x+28*x^2))/2. - _Michael Somos_, Jun 08 2000

%F n*a(n) = (12*n-18)*a(n-1)-28*(n-3)*a(n-2). - _Richard Choulet_, Dec 16 2009

%F a(n) ~ sqrt(3*sqrt(2)-2) * (2*(3+sqrt(2)))^n / (2*sqrt(14*Pi)*n^(3/2)). - _Vaclav Kotesovec_, Oct 11 2013

%t Rest[CoefficientList[Series[(1-Sqrt[1-12*x+28*x^2])/2, {x, 0, 20}], x]] (* _Vaclav Kotesovec_, Oct 11 2013 *)

%t 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 *)

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

%K nonn

%O 1,1

%A _Clark Kimberling_