OFFSET
0,2
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..200
FORMULA
a(n) = sum_{k=0..2n} T(n,k)*C(k,floor(k/2)), where T(n,k) is given by A027907.
a(n) = sum_{k=0..n} sum_{j=0..n} C(n,j)*C(j,k)*C(j+k,floor((j+k)/2)).
G.f.: ((3*x+1-(21*x^2-10*x+1)^(1/2))/(2*x*(3*x-4)*(7*x-1)))^(1/2). - Mark van Hoeij, Nov 16 2011
Conjecture: n*(2n+1)*a(n) +2(-61n^2+57n-20)*a(n-1) +3*(205n^2-523*n+346) * a(n-2) -72*(n-2)*(16n-33)*a(n-3) +567*(n-2)*(n-3)*a(n-4)=0. - R. J. Mathar, Dec 14 2011
a(n) ~ 7^(n+1/2)/sqrt(5*Pi*n). - Vaclav Kotesovec, Oct 24 2012
MATHEMATICA
CoefficientList[Series[((3*x+1-(21*x^2-10*x+1)^(1/2))/(2*x*(3*x-4)*(7*x-1)))^(1/2), {x, 0, 20}], x] (* Vaclav Kotesovec, Oct 24 2012 *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Feb 15 2005
STATUS
approved