|
%I #29 Sep 08 2022 08:44:39
%S 1,1623931,2900866919644,5135204548028317764,
%T 9097949506151746630368210,16117472448301015835209097979510,
%U 28553101725457044215054700034776694620
%N Gaussian binomial coefficient [ n,6 ] for q = -11.
%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 M. Sved, Gaussians and binomials, Ars. Combinatoria, 17A (1984), 325-351.
%H Vincenzo Librandi, <a href="/A015334/b015334.txt">Table of n, a(n) for n = 6..100</a>
%F G.f.: x^6/((1-x)*(1+11*x)*(1-121*x)*(1+1331*x)*(1-14641*x)*(1+161051*x)*(1-1771561*x)). - _Vincenzo Librandi_, Oct 30 2012
%F a(n) = (-1 +11^(6n-15) +198134223*11^(2n-9)*(1 -11^(2n-5)) +1330*11^(n-5)*(111 +111*11^(4n-10) -1637362*11^(2n-7))*(-1)^n) / 8011794142389510144000. - _Bruno Berselli_, Oct 30 2012
%t Table[QBinomial[n, 6, -11], {n, 6, 10}] (* _Vincenzo Librandi_, Oct 29 2012 *)
%o (Sage) [gaussian_binomial(n,6,-11) for n in range(6,13)] # _Zerinvary Lajos_, May 27 2009
%o (Magma) /* By definition: */ r:=6; q:=-11; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..12]]; // _Bruno Berselli_, Oct 30 2012
%K nonn,easy
%O 6,2
%A _Olivier Gérard_, Dec 11 1999
|
