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A006103 Gaussian binomial coefficient [ 2n,n ] for q=3.

%I A006103 M3715 #30 Sep 08 2022 08:44:34
%S A006103 1,4,130,33880,75913222,1506472167928,267598665689058580,
%T A006103 427028776969176679964080,6129263888495201102915629695046,
%U A006103 791614563787525746761491781638123230424,920094266641283414155073889843358388073398779900
%N A006103 Gaussian binomial coefficient [ 2n,n ] for q=3.
%D A006103 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.
%D A006103 I. P. Goulden and D. M. Jackson, Combinatorial Enumeration. Wiley, NY, 1983, p. 99.
%D A006103 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%D A006103 M. Sved, Gaussians and binomials, Ars. Combinatoria, 17A (1984), 325-351.
%H A006103 T. D. Noe, <a href="/A006103/b006103.txt">Table of n, a(n) for n = 0..25</a>
%H A006103 M. Sved, <a href="/A006095/a006095.pdf">Gaussians and binomials</a>, Ars. Combinatoria, 17A (1984), 325-351. (Annotated scanned copy)
%F A006103 a(n) = Sum_{k=0..n} 3^(k^2)*(A022167(n,k))^2. - _Werner Schulte_, Mar 09 2019
%t A006103 Table[QBinomial[2n, n, 3], {n, 0, 10}] (* _Vladimir Reshetnikov_, Sep 12 2016 *)
%o A006103 (PARI) q=3; {a(n) = prod(j=0, n-1, (1-q^(2*n-j))/(1-q^(j+1))) };
%o A006103 vector(15, n, n--; a(n)) \\ _G. C. Greubel_, Mar 09 2019
%o A006103 (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
%o A006103 (Sage) [gaussian_binomial(2*n,n,3) for n in (0..15)] # _G. C. Greubel_, Mar 09 2019
%Y A006103 Cf. A022167.
%K A006103 nonn,easy
%O A006103 0,2
%A A006103 _N. J. A. Sloane_