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 A015357 #29 Jun 30 2025 23:46:33
%S A015357 1,4921,36321901,229798289941,1526550040078063,9974653139743515223,
%T A015357 65533580739687859229563,429769342296322230713871283,
%U A015357 2820146424148466477944423359046,18502040831058043147238631145734166
%N A015357 Gaussian binomial coefficient [ n,8 ] for q=-3.
%D A015357 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 A015357 I. P. Goulden and D. M. Jackson, Combinatorial Enumeration. Wiley, NY, 1983, p. 99.
%D A015357 M. Sved, Gaussians and binomials, Ars. Combinatoria, 17A (1984), 325-351.
%H A015357 Vincenzo Librandi, <a href="/A015357/b015357.txt">Table of n, a(n) for n = 8..200</a>
%H A015357 <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (4921,12105660,-8513737740,-2091825362718,169437854380158,4524549298283340,-42209826451809660,-112576695670863081,150094635296999121).
%F A015357 a(n) = Product_{i=1..8} ((-3)^(n-i+1)-1)/((-3)^i-1). - _M. F. Hasler_, Nov 03 2012
%F A015357 G.f.: -x^8 / ( (x-1)*(27*x+1)*(81*x-1)*(729*x-1)*(9*x-1)*(2187*x+1)*(3*x+1)*(6561*x-1)*(243*x+1) ). - _R. J. Mathar_, Sep 02 2016
%F A015357 G.f. with offset 0: exp(Sum_{n >= 1} A015518(9*n)/A015518(n) * x^n/n) = 1 + 4921*x + 36321901*x^2 + .... - _Peter Bala_, Jun 29 2025
%t A015357 Table[QBinomial[n, 8, -3], {n, 8, 20}] (* _Vincenzo Librandi_, Nov 02 2012 *)
%o A015357 (Sage) [gaussian_binomial(n,8,-3) for n in range(8,18)] # _Zerinvary Lajos_, May 25 2009
%o A015357 (Magma) r:=8; q:=-3; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..25]]; // _Vincenzo Librandi_, Nov 02 2012
%o A015357 (PARI) A015357(n, r=8, q=-3)=prod(i=1, r, (1-q^(n-i+1))/(1-q^i)) \\ _M. F. Hasler_, Nov 03 2012
%Y A015357 Cf. Gaussian binomial coefficients [n,8] for q=-2..-13: A015356, A015359, A015360, A015361, A015363, A015364, A015365, A015367, A015368, A015369, A015370. - _M. F. Hasler_, Nov 03 2012
%Y A015357 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), this sequence (k = 8), A015375 (k = 9), A015388 (k = 10).
%K A015357 nonn,easy
%O A015357 8,2
%A A015357 _Olivier Gérard_