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.

A015405 Gaussian binomial coefficient [ n,11 ] for q=-2.

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%I A015405 #17 Sep 08 2022 08:44:39
%S A015405 1,-1365,3727815,-6785865905,14824402656063,-29439916001972385,
%T A015405 61250446192484546335,-124468028808034701006945,
%U A015405 255910660218571393553843871,-523082886040328458081329117025
%N A015405 Gaussian binomial coefficient [ n,11 ] for q=-2.
%D A015405 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 A015405 I. P. Goulden and D. M. Jackson, Combinatorial Enumeration. Wiley, NY, 1983, p. 99.
%D A015405 M. Sved, Gaussians and binomials, Ars. Combinatoria, 17A (1984), 325-351.
%H A015405 Vincenzo Librandi, <a href="/A015405/b015405.txt">Table of n, a(n) for n = 11..200</a>
%H A015405 <a href="/index/Ga#Gaussian_binomial_coefficients">Index entries related to Gaussian binomial coefficients</a>.
%F A015405 a(n) = Product_{i=1..11} ((-2)^(n-i+1)-1)/((-2)^i-1). - _Vincenzo Librandi_, Nov 05 2012
%t A015405 Table[QBinomial[n, 11, -2], {n, 11, 20}] (* _Vincenzo Librandi_, Nov 05 2012 *)
%o A015405 (Sage) [gaussian_binomial(n,11,-2) for n in range(11,21)] # _Zerinvary Lajos_, May 28 2009
%o A015405 (Magma) r:=11; q:=-2; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..25]]; // _Vincenzo Librandi_, Nov 05 2012
%Y A015405 Diagonal k=11 of the triangular array A015109. See there for further references and programs. - _M. F. Hasler_, Nov 04 2012
%K A015405 sign,easy
%O A015405 11,2
%A A015405 _Olivier Gérard_