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%I M5384 #40 Dec 31 2022 11:46:13
%S 1,121,11011,925771,75913222,6174066262,500777836042,40581331447162,
%T 3287582741506063,266307564861468823,21571273555248777493,
%U 1747282899667791058573,141530177899268957392924,11463951511551877750726204,928580264181940191843785764,75215006575885931519565302404
%N Gaussian binomial coefficient [ n,4 ] for q=3.
%D 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.
%D I. P. Goulden and D. M. Jackson, Combinatorial Enumeration. Wiley, NY, 1983, p. 99.
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%D M. Sved, Gaussians and binomials, Ars. Combinatoria, 17A (1984), 325-351.
%H T. D. Noe, <a href="/A006102/b006102.txt">Table of n, a(n) for n=4..100</a>
%H Simon Plouffe, <a href="https://arxiv.org/abs/0911.4975">Approximations de séries génératrices et quelques conjectures</a>, Dissertation, Université du Québec à Montréal, 1992; arXiv:0911.4975 [math.NT], 2009.
%H Simon Plouffe, <a href="/A000051/a000051_2.pdf">1031 Generating Functions</a>, Appendix to Thesis, Montreal, 1992
%H M. Sved, <a href="/A006095/a006095.pdf">Gaussians and binomials</a>, Ars. Combinatoria, 17A (1984), 325-351. (Annotated scanned copy)
%p A006102:=-1/((z-1)*(81*z-1)*(3*z-1)*(9*z-1)*(27*z-1)); # conjectured (correctly) by _Simon Plouffe_ in his 1992 dissertation
%t Table[QBinomial[n, 4, 3], {n, 4, 24}] (* _Vincenzo Librandi_, Aug 02 2016 *)
%o (Sage) [gaussian_binomial(n,4,3) for n in range(4,20)] # _Zerinvary Lajos_, May 25 2009
%o (Magma) r:=4; q:=3; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..20]]; // _Vincenzo Librandi_, Aug 02 2016
%Y Partial sums of A226804. - _Christian Krause_, Dec 26 2022
%K nonn
%O 4,2
%A _N. J. A. Sloane_
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