OFFSET
0,3
COMMENTS
a(n)=K(4,4; n)/4 with K(a,b; n) defined in a comment to A068763.
LINKS
Fung Lam, Table of n, a(n) for n = 0..925
FORMULA
a(n)=(4^n)*p(n, -3/4) with the row polynomials p(n, x) defined from array A068763.
a(n+1)= 4*sum(a(k)*a(n-k), k=0..n), n>=1, a(0)=1=a(1).
G.f.: (1-sqrt(1-16*x*(1-3*x)))/(8*x).
Recurrence: (n+1)*a(n) = 48*(2-n)*a(n-2) + 8*(2*n-1)*a(n-1). - Fung Lam, Mar 04 2014
a(n) ~ sqrt(6) * 12^n / (4*sqrt(Pi)*n^(3/2)). - Vaclav Kotesovec, Mar 04 2014
a(n) = 2^n*GegenbauerC(n-1, -n, -2)/(2*n) for n>=1. - Peter Luschny, May 09 2016
MAPLE
a := n -> `if`(n=0, 1, simplify(2^n*GegenbauerC(n-1, -n, -2))/(2*n)):
seq(a(n), n=0..19); # Peter Luschny, May 09 2016
MATHEMATICA
CoefficientList[Series[(1-Sqrt[1-16*x*(1-3*x)])/(8*x), {x, 0, 20}], x] (* Vaclav Kotesovec, Mar 04 2014 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Wolfdieter Lang, Mar 04 2002
STATUS
approved
