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.

A015407 Gaussian binomial coefficient [ n,11 ] for q=-3.

This page as a plain text file.
%I A015407 #20 Sep 08 2022 08:44:39
%S A015407 1,-132860,26477735830,-4522934399547980,811239619864365082573,
%T A015407 -143119691677080990521708240,25388050075285266699527263288120,
%U A015407 -4495361402895546052989488899628855120
%N A015407 Gaussian binomial coefficient [ n,11 ] for q=-3.
%D A015407 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 A015407 I. P. Goulden and D. M. Jackson, Combinatorial Enumeration. Wiley, NY, 1983, p. 99.
%D A015407 M. Sved, Gaussians and binomials, Ars. Combinatoria, 17A (1984), 325-351.
%H A015407 Vincenzo Librandi, <a href="/A015407/b015407.txt">Table of n, a(n) for n = 11..200</a>
%F A015407 a(n) = Product_{i=1..11} ((-3)^(n-i+1)-1)/((-3)^i-1) (by definition). - _Vincenzo Librandi_, Nov 05 2012
%t A015407 Table[QBinomial[n, 11, -3], {n, 11, 20}] (* _Vincenzo Librandi_, Nov 05 2012 *)
%o A015407 (Sage) [gaussian_binomial(n,11,-3) for n in range(11,19)] # _Zerinvary Lajos_, May 28 2009
%o A015407 (Magma) r:=11; q:=-3; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..25]]; // _Vincenzo Librandi_, Nov 05 2012
%K A015407 sign,easy
%O A015407 11,2
%A A015407 _Olivier Gérard_