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.

0, 1, 2, 0, 2, 4, 2, 12, 18, 24, 82, 120, 242, 620, 1010, 2324, 5154, 9520, 22178, 46512, 94178, 214548, 446690, 952732, 2122034, 4475592, 9776626, 21491496, 46096338, 101585276, 222360530, 483573796, 1068438594, 2341596256, 5140674882, 11369018464

Offset: 1

Author

Clark Kimberling

Keywords

• nonn

Programs

PARI

a(n)=polcoeff((x^2-sqrt(1-2*x^2-8*x^3+x^4+x*O(x^n)))/2,n)

Formula

G.f.: (1+x^2-sqrt(1-2*x^2-8*x^3+x^4))/2. - Michael Somos, Jun 08 2000

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