OFFSET
1,4
COMMENTS
As n -> infinity, a(2n)/a(2n-1) -> 9/2 and a(2n+1)/a(2n) -> 3/2.
LINKS
Robert Israel, Table of n, a(n) for n = 1..2415
FORMULA
a(n)=Sum(Binomial(n+j-1,j-1),(j,1,Floor[n/2])).
a(n) = floor(n/2) * C(n+floor(n/2), floor(n/2)) / (n+1). - Vaclav Kotesovec, Mar 02 2014
From Robert Israel, Feb 15 2019: (Start)(2*n+4)*a(n+1) = (3*n+2)*a(n) if n is even.
2*(n+2)*(n-1)*a(n+1) = 3*(n+1)*(3*n+1)*a(n) if n is odd. (End)
MAPLE
f:= proc(n) option remember;
if n::odd then (3*n-1)/(2*n+2)*procname(n-1)
else 3*n*(3*n-2)*procname(n-1)/(2*(n+1)*(n-2)) fi
end proc:
f(1):= 0: f(2):= 1: f(3):= 1:
map(f, [$1..40]); # Robert Israel, Feb 15 2019
MATHEMATICA
f[n_] := Sum[ Binomial[n + j - 1, j - 1], {j, n/2}]; Array[f, 30]
CROSSREFS
KEYWORD
nonn
AUTHOR
Roger L. Bagula, Dec 03 2010
STATUS
approved