

A015033


qCatalan numbers (binomial version) for q=3.


1



1, 1, 10, 847, 627382, 4138659802, 244829520301060, 130191700295480695111, 622829375926755523108996006, 26812578369717035183629988539429726, 10387976772168532331015929118843873280496300
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OFFSET

0,3


LINKS

G. C. Greubel, Table of n, a(n) for n = 0..46


FORMULA

a(n) = binomial(2*n, n, q)/(n+1)_q, where binomial(n,m,q) is the qbinomial coefficient, with q=3.
a(n) = ((1q)/(1q^(n+1)))*Product_{k=0..(n1)} (1q^(2*nk))/(1q^(k+1)), with q=3.  G. C. Greubel, Nov 11 2018


MATHEMATICA

Table[2 QBinomial[2n, n, 3]/(3^(n+1)  1), {n, 0, 20}]


PROG

(PARI) q=3; for(n=0, 20, print1(((1q)/(1q^(n+1)))*prod(k=0, n1, (1q^(2*nk))/(1q^(k+1))), ", ")) \\ G. C. Greubel, Nov 11 2018
(MAGMA) q:=3; [1] cat [((1q)/(1q^(n+1)))*(&*[(1q^(2*nk))/(1q^(k+1)): k in [0..n1]]): n in [1..20]]; // G. C. Greubel, Nov 11 2018


CROSSREFS

Cf. A015030 (q=2).
Sequence in context: A246599 A006714 A203533 * A126677 A054328 A203590
Adjacent sequences: A015030 A015031 A015032 * A015034 A015035 A015036


KEYWORD

nonn,easy


AUTHOR

Olivier Gérard


STATUS

approved



