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.

A015272 Gaussian binomial coefficient [ n,3 ] for q = -5.

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%I A015272 #24 Apr 29 2022 18:32:38
%S A015272 1,-104,13546,-1679704,210302171,-26279294704,3285123767796,
%T A015272 -410635172794704,51329529054158421,-6416187820400919704,
%U A015272 802023560334345174046,-100252942972187432169704
%N A015272 Gaussian binomial coefficient [ n,3 ] for q = -5.
%D A015272 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 A015272 I. P. Goulden and D. M. Jackson, Combinatorial Enumeration. Wiley, NY, 1983, p. 99.
%D A015272 M. Sved, Gaussians and binomials, Ars. Combinatoria, 17A (1984), 325-351.
%H A015272 Vincenzo Librandi, <a href="/A015272/b015272.txt">Table of n, a(n) for n = 3..200</a>
%H A015272 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (-104,2730,13000,-15625).
%F A015272 G.f.: x^3/((1-x)*(1+5*x)*(1-25*x)*(1+125*x)). - _Bruno Berselli_, Oct 29 2012
%F A015272 a(n) = (-1 + 21*5^(2n-3) + (-1)^n*5^(n-2)*(21-5^(2n-1)))/18144. - _Bruno Berselli_, Oct 29 2012
%t A015272 Table[QBinomial[n, 3, -5], {n, 3, 20}] (* _Vincenzo Librandi_, Oct 28 2012 *)
%t A015272 LinearRecurrence[{-104,2730,13000,-15625},{1,-104,13546,-1679704},20] (* _Harvey P. Dale_, Apr 29 2022 *)
%o A015272 (Sage) [gaussian_binomial(n,3,-5) for n in range(3,15)] # _Zerinvary Lajos_, May 27 2009
%K A015272 sign,easy
%O A015272 3,2
%A A015272 _Olivier Gérard_, Dec 11 1999