A103821 A Whitney transform of the central binomial coefficients A000984.

1, 3, 11, 43, 179, 771, 3395, 15171, 68515, 311907, 1428835, 6578531, 30414435, 141105251, 656588899, 3063038051, 14321092195, 67088405091, 314825048675, 1479654425187, 6963888239203, 32815960756835, 154813864252003

Offset

0,2

Comments

Partial sums of A006139. The Whitney transform maps the sequence with g.f. g(x) to that with g.f. (1/(1-x))g(x(1+x)).

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Formula

G.f. : 1/((1-x)sqrt(1-4x-4x^2));

a(n)=sum{k=0..n, sum{i=0..n, C(k, i-k)}*C(2k, k)}.

Conjecture: n*a(n) +(2-5n)*a(n-1) +2*a(n-2)+4*(n-1)*a(n-3)=0. - R. J. Mathar, Dec 14 2011

a(n) ~ sqrt(34+23*sqrt(2))*(2+2*sqrt(2))^n/(7*sqrt(Pi*n)). - Vaclav Kotesovec, Oct 17 2012

Mathematica

CoefficientList[Series[1/((1-x)*Sqrt[1-4*x-4*x^2]), {x, 0, 20}], x] (* Vaclav Kotesovec, Oct 17 2012 *)

Crossrefs

Sequence in context: A151093 A151094 A339043 * A151095 A219262 A196151

Adjacent sequences: A103818 A103819 A103820 * A103822 A103823 A103824

Keyword

easy,nonn

Author

Paul Barry, Feb 16 2005

Status

approved