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 A015375 #26 Jun 30 2025 23:46:26
%S A015375 1,-14762,326882347,-6204226946060,123644349019377043,
%T A015375 -2423717068608654822146,47771556642163840723529281,
%U A015375 -939857780045414554730512966640,18502040831058043147238631145734166,-364157167636884405223950738210339855212
%N A015375 Gaussian binomial coefficient [ n,9 ] for q=-3.
%D A015375 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 A015375 I. P. Goulden and D. M. Jackson, Combinatorial Enumeration. Wiley, NY, 1983, p. 99.
%D A015375 M. Sved, Gaussians and binomials, Ars. Combinatoria, 17A (1984), 325-351.
%H A015375 Vincenzo Librandi, <a href="/A015375/b015375.txt">Table of n, a(n) for n = 9..200</a>
%F A015375 a(n) = Product_{i=1..9} ((-3)^(n-i+1)-1)/((-3)^i-1) (by definition). - _Vincenzo Librandi_, Nov 04 2012
%F A015375 G.f.: -x^9 / ( (x-1)*(27*x+1)*(81*x-1)*(729*x-1)*(9*x-1)*(2187*x+1)*(3*x+1)*(19683*x+1)*(6561*x-1)*(243*x+1) ). - _R. J. Mathar_, Sep 02 2016
%F A015375 G.f. with offset 0: exp(Sum_{n >= 1} A015518(10*n)/A015518(n) * (-x)^n/n) = 1 - 14762*x + 326882347*x^2 + .... - _Peter Bala_, Jun 29 2025
%t A015375 Table[QBinomial[n, 9, -3],{n, 9, 20}] (* _Vincenzo Librandi_, Nov 04 2012 *)
%o A015375 (Sage) [gaussian_binomial(n,9,-3) for n in range(9,18)] # _Zerinvary Lajos_, May 25 2009
%o A015375 (Magma) r:=9; q:=-3; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..20]]; // _Vincenzo Librandi_, Nov 04 2012
%Y A015375 Cf. Gaussian binomial coefficients [n,9] for q=-2..-13: A015371, A015376, A015377, A015378, A015379, A015380, A015381, A015382, A015383, A015384, A015385. - _Vincenzo Librandi_, Nov 04 2012
%Y A015375 Gaussian binomial coefficient [n, k]_q for q = -3: A015251 (k = 2), A015268 (k = 3), A015288 (k = 4), A015306 (k = 5), A015324 (k = 6), A015340 (k = 7), A015357 (k = 8), this sequence (k = 9), A015388 (k = 10).
%K A015375 sign,easy
%O A015375 9,2
%A A015375 _Olivier Gérard_