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A015385 Gaussian binomial coefficient [ n,9 ] for q=-13. 23


%S 1,-9847035132,105044442632566365137,-1113436927250681654567602842120,

%T 11807854622717155763702496765310830475383,

%U -125216049699851612689080581288579246248342359563916

%N Gaussian binomial coefficient [ n,9 ] 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="/A015385/b015385.txt">Table of n, a(n) for n = 9..110</a>

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

%F a(n) = Product_{i=1..9} ((-13)^(n-i+1)-1)/((-13)^i-1). - M. F. Hasler, Nov 03 2012

%t Table[QBinomial[n, 9, -13],{n, 9, 20}] (* _Vincenzo Librandi_, Nov 04 2012 *)

%o (PARI) A015385(n,r=9,q=-13)=prod(i=1,r,(q^(n-i+1)-1)/(q^i-1)) \\ _M. F. Hasler_, Nov 03 2012

%o (MAGMA) r:=9; q:=-13; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..20]]; // _Vincenzo Librandi_, Nov 04 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), A015402 (r=10), A015422 (r=11), A015438 (r=12). - _M. F. Hasler_, Nov 03 2012

%Y Cf. Gaussian binomial coefficients [n, 9] for q = -2..-13: A015371, A015375, A015376, A015377, A015378, A015379, A015380, A015381, A015382, A015383, A015384. - _Vincenzo Librandi_, Nov 04 2012

%K sign,easy

%O 9,2

%A _Olivier GĂ©rard_

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Last modified February 17 23:35 EST 2020. Contains 332006 sequences. (Running on oeis4.)