A239488 Expansion of 1/x-4/(-sqrt(x^2-10*x+1)-x+1)-3.

6, 30, 186, 1290, 9582, 74550, 599730, 4948050, 41638614, 356007630, 3083837802, 27006251610, 238704231102, 2126733078630, 19079571337314, 172209370246050, 1562686251141030, 14248144422407550, 130467052593799962

Offset: 1

Author

Vladimir Kruchinin, Mar 20 2014

Keywords

• nonn

Crossrefs

Cf. A103210.

Programs

Maple

ogf := 1/x-4/(-sqrt(x^2-10*x+1)-x+1)-3;
series(ogf, x=0, 20): seq(coeff(%,x,n), n=0..19); # Peter Luschny, Mar 21 2014

Maxima

a(n):=sum(2^i*binomial(n,n-i+1)*binomial(n+i-1,n-1),i,0,n+1)/n;

Formula

a(n) = sum(i = 0..n+1, 2^i*binomial(n,n-i+1)*binomial(n+i-1,n-1))/n.

a(n) = T(2*n,n-1)/n where T(n,k) is triangle A116412.

D-finite with recurrence: (n+1)*a(n) +5*(-2*n+1)*a(n-1) +(n-2)*a(n-2)=0. a(n) = 2*A103210(n). - R. J. Mathar, May 23 2014