This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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 T. D. Noe, Table of n, a(n) for n = 0..25 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 Adjacent sequences:  A006100 A006101 A006102 * A006104 A006105 A006106 KEYWORD nonn,easy,changed AUTHOR STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified March 23 12:43 EDT 2019. Contains 321430 sequences. (Running on oeis4.)