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A006103 Gaussian binomial coefficient [ 2n,n ] for q=3.
(Formerly M3715)
1
1, 4, 130, 33880, 75913222, 1506472167928, 267598665689058580, 427028776969176679964080, 6129263888495201102915629695046, 791614563787525746761491781638123230424, 920094266641283414155073889843358388073398779900 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
REFERENCES
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.
LINKS
M. Sved, Gaussians and binomials, Ars. Combinatoria, 17A (1984), 325-351. (Annotated scanned copy)
FORMULA
a(n) = Sum_{k=0..n} 3^(k^2)*(A022167(n,k))^2. - Werner Schulte, Mar 09 2019
MATHEMATICA
Table[QBinomial[2n, n, 3], {n, 0, 10}] (* Vladimir Reshetnikov, Sep 12 2016 *)
PROG
(PARI) q=3; {a(n) = prod(j=0, n-1, (1-q^(2*n-j))/(1-q^(j+1))) };
vector(15, n, n--; a(n)) \\ G. C. Greubel, Mar 09 2019
(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
CROSSREFS
Cf. A022167.
Sequence in context: A096759 A299367 A299931 * A209012 A003371 A113253
KEYWORD
nonn,easy
AUTHOR
STATUS
approved

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Last modified April 20 12:09 EDT 2024. Contains 371838 sequences. (Running on oeis4.)