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.

A015310 Gaussian binomial coefficient [ n,5 ] for q = -6.

This page as a plain text file.
%I A015310 #25 Sep 08 2022 08:44:39
%S A015310 1,-6665,53308003,-412612541285,3210953026617931,
%T A015310 -24965159781954413525,194133243948726244454635,
%U A015310 -1509574711680960125598763925,11738459947705882553575280369515,-91278255494743382265330154281509525
%N A015310 Gaussian binomial coefficient [ n,5 ] for q = -6.
%D A015310 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 A015310 I. P. Goulden and D. M. Jackson, Combinatorial Enumeration. Wiley, NY, 1983, p. 99.
%D A015310 M. Sved, Gaussians and binomials, Ars. Combinatoria, 17A (1984), 325-351.
%H A015310 Vincenzo Librandi, <a href="/A015310/b015310.txt">Table of n, a(n) for n = 5..200</a>
%H A015310 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (-6665,8885778,1909009080,-69095809728,-403007063040,470184984576)
%F A015310 G.f.: -x^5 / ( (x-1)*(216*x+1)*(36*x-1)*(7776*x+1)*(1296*x-1)*(6*x+1) ). - _R. J. Mathar_, Aug 04 2016
%t A015310 Table[QBinomial[n, 5, -6], {n, 5, 20}] (* _Vincenzo Librandi_, Oct 29 2012 *)
%o A015310 (Sage) [gaussian_binomial(n,5,-6) for n in range(5,15)] # _Zerinvary Lajos_, May 27 2009
%o A015310 (Magma) r:=5; q:=-6; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..25]]; // _Vincenzo Librandi_, Aug 03 2016
%K A015310 sign,easy
%O A015310 5,2
%A A015310 _Olivier Gérard_, Dec 11 1999