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 A006099 Gaussian binomial coefficient [ n, n/2 ] for q=2. (Formerly M2700) 2
 1, 1, 3, 7, 35, 155, 1395, 11811, 200787, 3309747, 109221651, 3548836819, 230674393235, 14877590196755, 1919209135381395, 246614610741341843, 63379954960524853651, 16256896431763117598611, 8339787869494479328087443, 4274137206973266943778085267 (list; graph; refs; listen; history; text; internal format)
 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 EXTENSIONS More terms from Harvey P. Dale, Sep 07 2013 STATUS approved

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Last modified August 7 08:08 EDT 2020. Contains 336274 sequences. (Running on oeis4.)