A104598 Expansion of (1-z-sqrt(1-4z))/(1-4z)^2.

1, 10, 68, 394, 2092, 10516, 50920, 239962, 1107836, 5033020, 22572376, 100168260, 440604088, 1923626344, 8344694224, 35998921978, 154546983580, 660652406572, 2813422792696, 11940478362796, 50522190460072

Offset

1,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..200

D. Merlini, Generating functions for the area below some lattice paths, Discrete Mathematics and Theoretical Computer Science AC, 2003, 217-228.

Formula

Recurrence: n*(3*n-4)*a(n) = 2*(12*n^2-13*n-2)*a(n-1) - 8*(2*n-1)*(3*n-1) * a(n-2). - Vaclav Kotesovec, Oct 17 2012

a(n) ~ 3*2^(2*n-2)*n*(1-8/(3*sqrt(Pi)*sqrt(n))). - Vaclav Kotesovec, Oct 17 2012

a(n) = 2^(2*n-2)*(3*n+4)-(n+1)*C(2*n+1,n). - Vaclav Kotesovec, Oct 28 2012

Mathematica

Rest[CoefficientList[Series[(1-x-Sqrt[1-4*x])/(1-4*x)^2, {x, 0, 20}], x]] (* Vaclav Kotesovec, Oct 17 2012 *)
Table[2^(2*n-2)*(3*n+4)-(n+1)*Binomial[2*n+1, n], {n, 1, 20}] (* Vaclav Kotesovec, Oct 28 2012 *)

Crossrefs

Sequence in context: A280438 A192021 A026984 * A026901 A027242 A081656

Adjacent sequences: A104595 A104596 A104597 * A104599 A104600 A104601

Keyword

nonn

Author

Ralf Stephan, Mar 17 2005

Status

approved