cp's OEIS Frontend

A025251 a(n) = a(1)*a(n-1) + a(2)*a(n-2) + ... + a(n-3)*a(3) for n >= 4, with initial terms 0, 1, 2, 0.

%I A025251 #14 Jan 16 2025 11:15:05
%S A025251 0,1,2,0,2,4,2,12,18,24,82,120,242,620,1010,2324,5154,9520,22178,
%T A025251 46512,94178,214548,446690,952732,2122034,4475592,9776626,21491496,
%U A025251 46096338,101585276,222360530,483573796,1068438594,2341596256,5140674882,11369018464
%N A025251 a(n) = a(1)*a(n-1) + a(2)*a(n-2) + ... + a(n-3)*a(3) for n >= 4, with initial terms 0, 1, 2, 0.
%F A025251 G.f.: (1+x^2-sqrt(1-2*x^2-8*x^3+x^4))/2. - _Michael Somos_, Jun 08 2000
%F A025251 Conjecture: n*(n^2+n+1)*a(n) +(n-1)*(n^2+2*n+3)*a(n-1) -2*(n-3)*(n^2+n+1)*a(n-2) +2*(-5*n^3+16*n^2+19*n+30)*a(n-3) +(-7*n^3+23*n^2+59*n+126)*a(n-4) +(n-7)*(n^2+2*n+3)*a(n-5)=0. - _R. J. Mathar_, Feb 25 2015
%o A025251 (PARI) a(n)=polcoeff((x^2-sqrt(1-2*x^2-8*x^3+x^4+x*O(x^n)))/2,n)
%K A025251 nonn
%O A025251 1,3
%A A025251 _Clark Kimberling_