A025251 a(n) = a(1)*a(n-1) + a(2)*a(n-2) + ...+ a(n-3)*a(3) for n >= 4.

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

1,3

Links

Table of n, a(n) for n=1..36.

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

Prog

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

Crossrefs

Sequence in context: A291956 A023987 A021498 * A193334 A185081 A011119

Adjacent sequences: A025248 A025249 A025250 * A025252 A025253 A025254

Keyword

nonn

Author

Clark Kimberling

Status

approved