A006099 Gaussian binomial coefficient [ n, n/2 ] for q=2.

1, 1, 3, 7, 35, 155, 1395, 11811, 200787, 3309747, 109221651, 3548836819, 230674393235, 14877590196755, 1919209135381395, 246614610741341843, 63379954960524853651, 16256896431763117598611, 8339787869494479328087443, 4274137206973266943778085267

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

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..50.
• M. Sved, Gaussians and binomials, Ars. Combinatoria, 17A (1984), 325-351. (Annotated scanned copy)
• Eric Weisstein's World of Mathematics, q-Binomial Coefficient.

Crossrefs

Cf. A065446.

Programs

Mathematica

Table[QBinomial[n,Floor[n/2],2],{n,0,20}] (* Harvey P. Dale, Sep 07 2013 *)

Formula

a(n) ~ c * 2^(n^2/4), where c = 1 / QPochhammer[1/2, 1/2] = A065446 = 3.46274661945506361153795734292443116454... if n is even, and c = 2^(-1/4) / QPochhammer[1/2, 1/2] = 2^(-1/4) * A065446 = 2.911811219231681420726836976930855961516... if n is odd. - Vaclav Kotesovec, Jun 22 2014

Extensions

More terms from Harvey P. Dale, Sep 07 2013