A006099 Gaussian binomial coefficient [ n, n/2 ] for q=2. (Formerly M2700)

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

Offset

0,3

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.

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

Mathematica

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

Crossrefs

Cf. A065446.

Sequence in context: A147681 A055487 A121130 * A240272 A053530 A215575

Adjacent sequences: A006096 A006097 A006098 * A006100 A006101 A006102

Keyword

nonn

Author

N. J. A. Sloane

Extensions

More terms from Harvey P. Dale, Sep 07 2013

Status

approved