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A015033 q-Catalan numbers (binomial version) for q=3. 1
1, 1, 10, 847, 627382, 4138659802, 244829520301060, 130191700295480695111, 622829375926755523108996006, 26812578369717035183629988539429726, 10387976772168532331015929118843873280496300 (list; graph; refs; listen; history; text; internal format)
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 q-binomial coefficient, with q=3.

a(n) = ((1-q)/(1-q^(n+1)))*Product_{k=0..(n-1)} (1-q^(2*n-k))/(1-q^(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(((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:=3; [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: A246599 A006714 A203533 * A126677 A054328 A203590

Adjacent sequences:  A015030 A015031 A015032 * A015034 A015035 A015036

KEYWORD

nonn,easy

AUTHOR

Olivier Gérard

STATUS

approved

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Last modified April 11 14:58 EDT 2021. Contains 342886 sequences. (Running on oeis4.)