OFFSET
0,3
COMMENTS
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..200
FORMULA
G.f.: (1-5x-sqrt(1-10x+9x^2))/(8x); a(n)=sum{k=0..n-1, (1/n)*C(n,k)C(n,k+1)4^k}; a(n+1)=sum{k=0..floor(n/2), C(n, 2k)C(k)5^(n-2k)*4^k};
Recurrence: (n+1)*a(n) = 5*(2*n-1)*a(n-1) - 9*(n-2)*a(n-2). - Vaclav Kotesovec, Oct 19 2012
a(n) ~ 3^(2*n+1)/(4*sqrt(2*Pi)*n^(3/2)). - Vaclav Kotesovec, Oct 19 2012
a(n) = A059231(n) for n>0. - Philippe Deléham, Apr 03 2013
a(n) = hypergeom([1-n, -n], [2], 4) for n>0. - Peter Luschny, Sep 23 2014
MATHEMATICA
CoefficientList[Series[(1-5*x-Sqrt[1-10*x+9*x^2])/(8*x), {x, 0, 20}], x] (* Vaclav Kotesovec, Oct 19 2012 *)
PROG
(Sage)
A127846 = lambda n: hypergeometric([1-n, -n], [2], 4) if n>0 else 0
[Integer(A127846(n).n(100)) for n in (0..22)] # Peter Luschny, Sep 23 2014
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Feb 02 2007
STATUS
approved