A015370 - OEIS

%I #23 Sep 08 2022 08:44:39

%S 1,757464241,621564749363392901,506798783502833908602716981,

%T 413425812255544017749839936272484623,

%U 337243227617163445881817693983677965955870943,275099718210633054941121644140453635236773122223471523

%N Gaussian binomial coefficient [ n,8 ] 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="/A015370/b015370.txt">Table of n, a(n) for n = 8..100</a>

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

%F a(n) = Product_{i=1..8} ((-13)^(n-i+1)-1)/((-13)^i-1). - _M. F. Hasler_, Nov 03 2012

%t Table[QBinomial[n, 8, -13], {n, 8, 14}] (* _Vincenzo Librandi_, Nov 03 2012 *)

%o (Sage) [gaussian_binomial(n,8,-13) for n in range(8,14)] # _Zerinvary Lajos_, May 25 2009

%o (Magma) r:=8; q:=-13; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..18]]; // _Vincenzo Librandi_, Nov 03 2012

%o (PARI) A015370(n,r=8,q=-13)=prod(i=1,r,(q^(n-i+1)-1)/(q^i-1)) \\ _M. F. Hasler_, Nov 03 2012

%Y Cf. Gaussian binomial coefficients [n,8] for q=-2..-12: A015356, A015357, A015359, A015360, A015361, A015363, A015364, A015365, A015367, A015368, A015369. - _M. F. Hasler_, Nov 03 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), A015385 (r=9), A015402 (r=10), A015422 (r=11), A015438 (r=12). - _M. F. Hasler_, Nov 03 2012

%K nonn,easy

%O 8,2

%A _Olivier Gérard_