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A015030 q-Catalan numbers (binomial version) for q=2. 3
1, 1, 5, 93, 6477, 1733677, 1816333805, 7526310334829, 124031223014725741, 8152285307423733458541, 2140200604371078953284092525, 2245805993494514875022552272042605 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..57

FORMULA

a(n) = binomial(2*n, n, q)/(n+1)_q, where binomial(n,m,q) is the q-binomial coefficient, with q=2.

a(n) = ((1-q)/(1-q^(n+1)))*Product_{k=0..(n-1)} (1-q^(2*n-k))/(1-q^(k+1)), with q=2. - G. C. Greubel, Nov 11 2018

MATHEMATICA

Table[QBinomial[2n, n, 2]/(2^(n+1) - 1), {n, 0, 20}] (* Vladimir Reshetnikov, Sep 16 2016 *)

PROG

(PARI) q=2; 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:=2; [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

(Sage) from sage.combinat.q_analogues import q_catalan_number [q_catalan_number(n, 2) for n in range(20)] # G. C. Greubel, Nov 21 2018

CROSSREFS

Sequence in context: A000365 A209471 A012784 * A136097 A270071 A047052

Adjacent sequences:  A015027 A015028 A015029 * A015031 A015032 A015033

KEYWORD

nonn,easy

AUTHOR

Olivier Gérard

STATUS

approved

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Last modified January 28 13:26 EST 2020. Contains 331321 sequences. (Running on oeis4.)