OFFSET
0,2
COMMENTS
In general, f(n) = Sum_{k=0..floor(n/2)} C(2k,k)C(2(n-2k),n-2k)*r^k has g.f. 1/sqrt(1-4x-4r*x^2+16r*x^3).
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..200
Hacène Belbachir, Abdelghani Mehdaoui, and László Szalay, Diagonal Sums in the Pascal Pyramid, II: Applications, J. Int. Seq., Vol. 22 (2019), Article 19.3.5.
FORMULA
a(n)=sum{k=0..floor(n/2), C(2k, k)C(2(n-2k), n-2k)*(-1)^k}.
D-finite with recurrence: n*a(n)+2(1-2n)*a(n-1) +4(n-1)*a(n-2)+8(3-2n)*a(n-3)=0. - R. J. Mathar, Dec 08 2011
a(n) ~ 2^(2*n+1)/sqrt(5*Pi*n). - Vaclav Kotesovec, Feb 01 2014
MATHEMATICA
CoefficientList[Series[1/Sqrt[1-4x+4x^2-16x^3], {x, 0, 30}], x] (* Harvey P. Dale, May 17 2012 *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Apr 24 2005
STATUS
approved