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.
%I A015268 #35 Jul 04 2025 23:46:38
%S A015268 1,-20,610,-15860,433771,-11662040,315323620,-8509702520,229798289941,
%T A015268 -6204226946060,167517069529030,-4522934399547980,122119467087816511,
%U A015268 -3297223466672052080,89025052902439936840,-2403676254645238280240
%N A015268 Gaussian binomial coefficient [ n,3 ] for q = -3.
%D A015268 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 A015268 I. P. Goulden and D. M. Jackson, Combinatorial Enumeration. Wiley, NY, 1983, p. 99.
%D A015268 M. Sved, Gaussians and binomials, Ars. Combinatoria, 17A (1984), 325-351.
%H A015268 Vincenzo Librandi, <a href="/A015268/b015268.txt">Table of n, a(n) for n = 3..200</a>
%H A015268 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (-20,210,540,-729).
%F A015268 G.f.: x^3/((1-x)*(1+3*x)*(1-9*x)*(1+27*x)). - _Bruno Berselli_, Oct 29 2012
%F A015268 a(n) = (-1 + 7*3^(2n-3) + (-1)^n*3^(n-2)*(7-3^(2n-1)))/896. - _Bruno Berselli_, Oct 29 2012
%F A015268 G.f.: x^3 * exp(Sum_{n >= 1} A015518(4*n)/A015518(n) * (-x)^n/n) = x^3 * (1 - 20*x + 610*x^2 - ...). - _Peter Bala_, Jun 29 2025
%t A015268 Table[QBinomial[n, 3, -3], {n, 3, 20}] (* _Vincenzo Librandi_, Oct 28 2012 *)
%o A015268 (SageMath) [gaussian_binomial(n,3,-3) for n in range(3,19)] # _Zerinvary Lajos_, May 27 2009
%o A015268 (Magma) [(-1+7*3^(2*n-3)+(-1)^n*3^(n-2)*(7-3^(2*n-1)))/896: n in [3..18]]; // _Bruno Berselli_, Oct 29 2012
%o A015268 (Maxima) makelist(coeff(taylor(1/((1-x)*(1+3*x)*(1-9*x)*(1+27*x)), x, 0, n), x, n), n, 0, 15); /* _Bruno Berselli_, Oct 29 2012 */
%Y A015268 Gaussian binomial coefficient [n, k]_q for q = -3: A015251 (k = 2), this sequence (k = 3), A015288 (k = 4), A015306 (k = 5), A015324 (k = 6), A015340 (k = 7), A015357 (k = 8), A015375 (k = 9), A015388 (k = 10).
%Y A015268 Cf. A015518.
%K A015268 sign,easy
%O A015268 3,2
%A A015268 _Olivier Gérard_, Dec 11 1999