A025254 a(n) = a(1)*a(n-1) + a(2)*a(n-2) + ...+ a(n-3)*a(3) for n >= 4.

3, 1, 1, 3, 10, 34, 118, 417, 1497, 5448, 20063, 74649, 280252, 1060439, 4040413, 15488981, 59701236, 231236830, 899559100, 3513314664, 13770811198, 54152480421, 213585706927, 844723104691, 3349274471386, 13310603555085, 53012829376985

Offset

1,1

Links

Table of n, a(n) for n=1..27.

Formula

G.f.: (1 + 3*x + x^2 - sqrt(x^4 + 2*x^3 + 7*x^2 - 6*x + 1))/(2*x). - Vaclav Kotesovec, Mar 02 2014

Recurrence: (n+1)*a(n) = 3*(2*n-1)*a(n-1) - 7*(n-2)*a(n-2) - (2*n-7)*a(n-3) - (n-5)*a(n-4). - Vaclav Kotesovec, Mar 02 2014

Mathematica

CoefficientList[Series[(1+3*x+x^2-Sqrt[x^4+2*x^3+7*x^2-6*x+1])/(2*x), {x, 0, 20}], x] (* Vaclav Kotesovec, Mar 02 2014 *)

Crossrefs

Cf. A178578.

Sequence in context: A014516 A247306 A016563 * A245537 A277198 A242735

Adjacent sequences: A025251 A025252 A025253 * A025255 A025256 A025257

Keyword

nonn

Author

Clark Kimberling

Status

approved