A247171 G.f.: (2*x^2+4*x+3)/((2*x+2)*sqrt(-4*x^3-4*x^2+1))-1/(2*x+2).

1, 1, 3, 4, 11, 21, 48, 106, 235, 535, 1203, 2751, 6272, 14392, 33078, 76224, 176043, 407253, 943833, 2190397, 5090371, 11843689, 27586793, 64320191, 150102784, 350586496, 819477792, 1916861350, 4486760870, 10508582130, 24626700888

Offset: 0

Author

Vladimir Kruchinin, Nov 22 2014

Keywords

• nonn

Crossrefs

Cf. A007477.

Programs

Mathematica

CoefficientList[Series[(2 x^2 + 4 x + 3) / ((2 x + 2) Sqrt[-4 x^3 - 4 x^2 + 1]) - 1 / (2 x + 2), {x, 0, 40}], x] (* Vincenzo Librandi, Nov 22 2014 *)

Maxima

a(n):=if n=0 then 1 else n*sum((binomial(2*k,n-k)*binomial(n-k-1,k-1))/k,k,1,n);

Formula

a(n) = n*Sum_{k=1..n} (binomial(2*k,n-k)*binomial(n-k-1,k-1))/k, n>0, a(0)=1.

D-finite with recurrence: 3*n*a(n) +(7*n-8)*a(n-1) +2*(-3*n-2)*a(n-2) +2*(-19*n+35)*a(n-3) +2*(-26*n+81)*a(n-4) +4*(-8*n+35)*a(n-5) +4*(-2*n+11)*a(n-6)=0. - R. J. Mathar, Jan 25 2020