cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A015393 Gaussian binomial coefficient [ n,10 ] for q=-7.

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%I A015393 #19 Sep 08 2022 08:44:39
%S A015393 1,247165843,71272779562356450,20074270583791406305395150,
%T A015393 5672847283550509352791825564114953,
%U A015393 1602343611088456383646516751967506297398179,452626257785468649545785666454333613632908777305800
%N A015393 Gaussian binomial coefficient [ n,10 ] for q=-7.
%D A015393 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 A015393 I. P. Goulden and D. M. Jackson, Combinatorial Enumeration. Wiley, NY, 1983, p. 99.
%D A015393 M. Sved, Gaussians and binomials, Ars. Combinatoria, 17A (1984), 325-351.
%H A015393 Vincenzo Librandi, <a href="/A015393/b015393.txt">Table of n, a(n) for n = 10..130</a>
%F A015393 a(n) = Product_{i=1..10} ((-7)^(n-i+1)-1)/((-7)^i-1) (by definition). - _Vincenzo Librandi_, Nov 04 2012
%t A015393 Table[QBinomial[n, 10, -7], {n, 10, 20}] (* _Vincenzo Librandi_, Nov 04 2012 *)
%o A015393 (Sage) [gaussian_binomial(n,10,-7) for n in range(10,16)] # _Zerinvary Lajos_, May 25 2009
%o A015393 (Magma) r:=10; q:=-7; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..25]]; // _Vincenzo Librandi_, Nov 04 2012
%Y A015393 Cf. Gaussian binomial coefficients [n, 10] for q = -2..-13: A015386, A015388, A015390, A015391, A015392, A015394, A015397, A015398, A015399, A015401, A015402. - _Vincenzo Librandi_, Nov 04 2012
%K A015393 nonn,easy
%O A015393 10,2
%A A015393 _Olivier Gérard_