A103821 - OEIS

%I #11 May 13 2013 01:30:47

%S 1,3,11,43,179,771,3395,15171,68515,311907,1428835,6578531,30414435,

%T 141105251,656588899,3063038051,14321092195,67088405091,314825048675,

%U 1479654425187,6963888239203,32815960756835,154813864252003

%N A Whitney transform of the central binomial coefficients A000984.

%C 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)).

%H Vincenzo Librandi, <a href="/A103821/b103821.txt">Table of n, a(n) for n = 0..200</a>

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

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

%F 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

%F a(n) ~ sqrt(34+23*sqrt(2))*(2+2*sqrt(2))^n/(7*sqrt(Pi*n)). - _Vaclav Kotesovec_, Oct 17 2012

%t CoefficientList[Series[1/((1-x)*Sqrt[1-4*x-4*x^2]), {x, 0, 20}], x] (* _Vaclav Kotesovec_, Oct 17 2012 *)

%K easy,nonn

%O 0,2

%A _Paul Barry_, Feb 16 2005