OFFSET
0,3
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..41
FORMULA
a(n) = binomial(2*n, n, q)/(n+1)_q, where binomial(n,m,q) is the q-binomial coefficient, with q=4.
a(n) = ((1-q)/(1-q^(n+1)))*Product_{k=0..(n-1)} (1-q^(2*n-k))/(1-q^(k+1)), with q=4. - G. C. Greubel, Nov 11 2018
MATHEMATICA
Table[3*QBinomial[2 n, n, 4]/(4^(n + 1) - 1), {n, 0, 20}] (* G. C. Greubel, Nov 11 2018 *)
PROG
(PARI) q=4; for(n=0, 20, print1(((1-q)/(1-q^(n+1)))*prod(k=0, n-1, (1-q^(2*n-k))/(1-q^(k+1))), ", ")) \\ G. C. Greubel, Nov 11 2018
(Magma) q:=4; [1] cat [((1-q)/(1-q^(n+1)))*(&*[(1-q^(2*n-k))/(1-q^(k+1)): k in [0..n-1]]): n in [1..20]]; // G. C. Greubel, Nov 11 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved