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
T. D. Noe, Table of n, a(n) for n = 0..35
Alin Bostan and Sergey Yurkevich, On the q-analogue of Pólya's Theorem, arXiv:2109.02406 [math.CO], 2021.
I. Siap and I. Aydogdu, Counting The Generator Matrices of Z_2 Z_8 Codes, arXiv:1303.6985 [math.CO], 2013.
M. Sved, Gaussians and binomials, Ars. Combinatoria, 17A (1984), 325-351. (Annotated scanned copy)
Eric Weisstein's World of Mathematics, q-Binomial Coefficient.
FORMULA
a(n) = A022166(2n,n). - Alois P. Heinz, Mar 30 2016
a(n) ~ c * 2^(n^2), where c = A065446. - Vaclav Kotesovec, Sep 22 2016
a(n) = Sum_{k=0..n} 2^(k^2)*(A022166(n,k))^2. - Werner Schulte, Mar 09 2019
MATHEMATICA
Table[QBinomial[2n, n, 2], {n, 0, 20}] (* Harvey P. Dale, Oct 22 2012 *)
PROG
(Sage) [gaussian_binomial(2*n, n, 2) for n in range(0, 11)] # Zerinvary Lajos, May 25 2009
(PARI) q=2; {a(n) = prod(j=0, n-1, (1-q^(2*n-j))/(1-q^(j+1))) };
vector(10, n, n--; a(n)) \\ G. C. Greubel, Mar 09 2019
(Magma) q:=2; [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
CROSSREFS
KEYWORD
nonn,changed
AUTHOR
EXTENSIONS
More terms from Harvey P. Dale, Oct 22 2012
STATUS
approved