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 A015340 #25 Jun 30 2025 23:46:37
%S A015340 1,-1640,4035220,-8509702520,18843459775162,-41041673208656120,
%T A015340 89881489830655851460,-196480936769813691291560,
%U A015340 429769342296322230713871283,-939857780045414554730512966640
%N A015340 Gaussian binomial coefficient [ n,7 ] for q = -3.
%D A015340 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 A015340 I. P. Goulden and D. M. Jackson, Combinatorial Enumeration. Wiley, NY, 1983, p. 99.
%D A015340 M. Sved, Gaussians and binomials, Ars. Combinatoria, 17A (1984), 325-351.
%H A015340 Vincenzo Librandi, <a href="/A015340/b015340.txt">Table of n, a(n) for n = 7..200</a>
%H A015340 <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (-1640,1345620,314875080,-25929962838,-688631799960,6436058745780,17154979252920,-22876792454961).
%F A015340 G.f.: x^7 / ( (x-1)*(27*x+1)*(81*x-1)*(729*x-1)*(9*x-1)*(2187*x+1)*(3*x+1)*(243*x+1) ). - _R. J. Mathar_, Sep 02 2016
%F A015340 G.f. with offset 0: exp(Sum_{n >= 1} A015518(8*n)/A015518(n) * (-x)^n/n) = 1 - 1640*x + 4035220*x^2 - .... - _Peter Bala_, Jun 29 2025
%t A015340 Table[QBinomial[n, 7, -3], {n, 7, 20}] (* _Vincenzo Librandi_, Oct 29 2012 *)
%o A015340 (Sage) [gaussian_binomial(n,7,-3) for n in range(7,17)] # _Zerinvary Lajos_, May 27 2009
%Y A015340 Gaussian binomial coefficient [n, k]_q for q = -3: A015251 (k = 2), A015268 (k = 3), A015288 (k = 4), A015306 (k = 5), A015324 (k = 6), this sequence (k = 7), A015357 (k = 8), A015375 (k = 9), A015388 (k = 10).
%K A015340 sign,easy
%O A015340 7,2
%A A015340 _Olivier Gérard_, Dec 11 1999