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.

A015288 Gaussian binomial coefficient [ n,4 ] for q = -3.

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%I A015288 #23 Sep 08 2022 08:44:39
%S A015288 1,61,5551,433771,35569222,2869444942,232740363922,18843459775162,
%T A015288 1526550040078063,123644349019377043,10015359787639069513,
%U A015288 811239619864365082573,65710531328480659504924
%N A015288 Gaussian binomial coefficient [ n,4 ] for q = -3.
%D A015288 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 A015288 I. P. Goulden and D. M. Jackson, Combinatorial Enumeration. Wiley, NY, 1983, p. 99.
%D A015288 M. Sved, Gaussians and binomials, Ars. Combinatoria, 17A (1984), 325-351.
%H A015288 Vincenzo Librandi, <a href="/A015288/b015288.txt">Table of n, a(n) for n = 4..500</a>
%H A015288 <a href="/index/Ga#Gaussian_binomial_coefficients">Index entries related to Gaussian binomial coefficients</a>.
%H A015288 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (61,1830,-16470,-44469,59049).
%F A015288 G.f.: -x^4 / ( (x-1)*(27*x+1)*(81*x-1)*(9*x-1)*(3*x+1) ). - _R. J. Mathar_, Aug 03 2016
%t A015288 Table[QBinomial[n, 4, -3], {n, 4, 20}] (* _Vincenzo Librandi_, Oct 28 2012 *)
%o A015288 (Sage) [gaussian_binomial(n,4,-3) for n in range(4,17)] # _Zerinvary Lajos_, May 27 2009
%o A015288 (Magma) r:=4; q:=-3; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..20]]; // _Vincenzo Librandi_, Aug 02 2016
%K A015288 nonn,easy
%O A015288 4,2
%A A015288 _Olivier Gérard_, Dec 11 1999