A015034 q-Catalan numbers (binomial version) for q=4.

1, 1, 17, 4433, 18245201, 1197172898385, 1255709588423576145, 21068918017101222558779985, 5655752483351603939678821837720145, 24291387778773301588924456932322615789898321

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

Cf. A015030 (q=2).

Sequence in context: A329168 A194015 A015058 * A350980 A161583 A013722

Adjacent sequences: A015031 A015032 A015033 * A015035 A015036 A015037

Keyword

nonn,easy

Author

Olivier Gérard

Status

approved