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 A015438 Gaussian binomial coefficient [ n,12 ] for q=-13. 12

%I

%S 1,21633936185161,507029461102251552321630151,

%T 11807441196984503845077844573952807835871,

%U 275100402115798836253928241395289617394098490488956444,6409295323626866454933457428954320223001885025904687118646704057084

%N Gaussian binomial coefficient [ n,12 ] for q=-13.

%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="/A015438/b015438.txt">Table of n, a(n) for n = 12..80</a>

%H <a href="/index/Ga#Gaussian_binomial_coefficients">Index entries related to Gaussian binomial coefficients</a>.

%F a(n)=product_{i=1..12} ((-13)^(n-i+1)-1)/((-13)^i-1). - M. F. Hasler, Nov 03 2012

%t Table[QBinomial[n, 12, -13], {n, 12, 20}] (* _Vincenzo Librandi_, Nov 06 2012 *)

%o (Sage) [gaussian_binomial(n,12,-13) for n in range(12,17)] # _Zerinvary Lajos_, May 28 2009

%o (PARI) A015438(n,r=12,q=-13)=prod(i=1,r,(q^(n-i+1)-1)/(q^i-1)) \\ _M. F. Hasler_, Nov 03 2012

%o (MAGMA) r:=12; q:=-13; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..20]]; // _Vincenzo Librandi_, Nov 06 2012

%Y Cf. Gaussian binomial coefficients [n,r] for q=-13: A015265 (r=2), A015286 (r=3), A015303 (r=4), A015321 (r=5), A015337 (r=6), A015355 (r=7), A015370 (r=8), A015385 (r=9), A015402 (r=10), A015422 (r=11). - _M. F. Hasler_, Nov 03 2012

%K nonn,easy

%O 12,2