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A006103
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Gaussian binomial coefficient [ 2n,n ] for q=3.
(Formerly M3715)
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1
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1, 4, 130, 33880, 75913222, 1506472167928, 267598665689058580, 427028776969176679964080, 6129263888495201102915629695046, 791614563787525746761491781638123230424, 920094266641283414155073889843358388073398779900
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OFFSET
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0,2
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REFERENCES
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J. Goldman and G.-C. Rota, The number of subspaces of a vector space, pp. 75-83 of W. T. Tutte, editor, Recent Progress in Combinatorics. Academic Press, NY, 1969.
I. P. Goulden and D. M. Jackson, Combinatorial Enumeration. Wiley, NY, 1983, p. 99.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
M. Sved, Gaussians and binomials, Ars. Combinatoria, 17A (1984), 325-351.
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LINKS
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FORMULA
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MATHEMATICA
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PROG
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(PARI) q=3; {a(n) = prod(j=0, n-1, (1-q^(2*n-j))/(1-q^(j+1))) };
(Magma) q:=3; [n le 0 select 1 else (&*[(1-q^(2*n-j))/(1-q^(j+1)): j in [0..n-1]]): n in [0..15]]; // G. C. Greubel, Mar 09 2019
(Sage) [gaussian_binomial(2*n, n, 3) for n in (0..15)] # G. C. Greubel, Mar 09 2019
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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