A247162 G.f. 1-(2*x^3)/(-sqrt(-3*x^4-4*x^3-2*x^2+1)-x^2+1).

1, 0, 1, 0, 1, 1, 2, 3, 6, 10, 19, 35, 66, 125, 240, 462, 897, 1750, 3431, 6756, 13357, 26499, 52744, 105292, 210761, 422928, 850631, 1714505, 3462538, 7005661, 14198718, 28823497, 58600076, 119306476, 243224949, 496475106, 1014616271

Offset

1,7

Links

Table of n, a(n) for n=1..37.

Formula

a(n) = sum(k=1..n, (sum(j=0..k, binomial(j,n-k-j)*binomial(k,j)) * binomial(n-k-2,k-1))/k).

D-finite with recurrence: (n-1)*n*a(n) = 6*(n-8)*(n-7)*a(n-7) + 2*(5+7*(n-7))*(n-7)*a(n-6) + (24+43*(n-7)+15*(n-7)^2)*a(n-5) + (84+63*(n-7)+11*(n-7)^2)*a(n-4) + (90+40*(n-7)+4*(n-7)^2)*a(n-3) + (30+ 6*(n-7))*a(n-2) - (n-2)*(n-1)*a(n-1). - Benedict W. J. Irwin, Sep 25 2016

D-finite with recurrence: n*a(n) = -a(n-1) + (2*n - 5)*a(n-2) + (4*n - 17)*a(n-3) + 3*(n-5)*a(n-4). - Vaclav Kotesovec, Sep 25 2016

Mathematica

Rest[CoefficientList[Series[(1+z(2+z)-Sqrt[-(1+z)(-1+z+z^2+3z^3)])/(2(1+z)), {z, 0, 30}], z]] (* Benedict W. J. Irwin, Sep 25 2016 *)

Prog

(Maxima)
a(n):=sum(((sum(binomial(j, n-k-j)*binomial(k, j), j, 0, k))*binomial(n-k-2, k-1))/k, k, 1, n);

Crossrefs

Sequence in context: A000693 A054178 A005833 * A001678 A346787 A113292

Adjacent sequences: A247159 A247160 A247161 * A247163 A247164 A247165

Keyword

nonn

Author

Vladimir Kruchinin, Nov 21 2014

Status

approved