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 A015308 #39 Dec 30 2024 21:53:58
%S A015308 1,-819,894621,-901984419,927257668701,-948584595081123,
%T A015308 971588061067577437,-994845394688060798883,1018737244037427165087837,
%U A015308 -1043182954580986851130914723,1068220365220113899181567068253
%N A015308 Gaussian binomial coefficient [ n,5 ] for q = -4.
%D A015308 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 A015308 I. P. Goulden and D. M. Jackson, Combinatorial Enumeration. Wiley, NY, 1983, p. 99.
%D A015308 M. Sved, Gaussians and binomials, Ars. Combinatoria, 17A (1984), 325-351.
%H A015308 Vincenzo Librandi, <a href="/A015308/b015308.txt">Table of n, a(n) for n = 5..200</a>
%H A015308 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (-819,223860,14051520,-229232640,-858783744,1073741824).
%F A015308 a(n) = Product_{i=1..5} ((-4)^(n-i+1)-1)/((-4)^i-1), by definition. - _Vincenzo Librandi_, Aug 03 2016
%F A015308 G.f.: x^5/((1-x)*(1+4*x)*(1-16*x)*(1+64*x)*(1-256*x)*(1+1024*x)). - _R. J. Mathar_, Aug 04 2016
%F A015308 From _G. C. Greubel_, Sep 21 2019: (Start)
%F A015308 a(n) = (1 - 205*(-4)^(n-4) + 3485*(-4)^(2*n-7) - 3485*(-4)^(3*n-9) + 205*(-4)^(4*n-10) - (-4)^(5*n-10))/1274203125.
%F A015308 E.g.f.: exp(-1024*x)*(-1 + 13940*exp(960*x) - 839680*exp(1020*x) + 1048576*exp(1025*x) - 223040*exp(1040*x) + 205*exp(1280*x))/1336098816000000. (End)
%p A015308 seq((1 -205*(-4)^(n-4) +3485*(-4)^(2*n-7) -3485*(-4)^(3*n-9) +205*(-4)^(4*n-10) -(-4)^(5*n-10))/1274203125, n=5..25); # _G. C. Greubel_, Sep 21 2019
%t A015308 Table[QBinomial[n, 5, -4], {n, 5, 20}] (* _Vincenzo Librandi_, Oct 29 2012 *)
%o A015308 (Sage) [gaussian_binomial(n,5,-4) for n in range(5,16)] # _Zerinvary Lajos_, May 27 2009
%o A015308 (Magma) r:=5; q:=-4; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..25]]; // _Vincenzo Librandi_, Aug 03 2016
%o A015308 (PARI) a(n) = (1 -205*(-4)^(n-4) +3485*(-4)^(2*n-7) -3485*(-4)^(3*n-9) +205*(-4)^(4*n-10) -(-4)^(5*n-10))/1274203125; \\ _G. C. Greubel_, Sep 21 2019
%o A015308 (GAP) List([5..25], n-> (1 -205*(-4)^(n-4) +3485*(-4)^(2*n-7) -3485*(-4)^(3*n-9) +205*(-4)^(4*n-10) -(-4)^(5*n-10))/1274203125); # _G. C. Greubel_, Sep 21 2019
%Y A015308 Gaussian binomial coefficients [n,5]: A015305 (q=-2), A015306(q=-3), this sequence (q=-4), A015309 (q=-5), A015310 (q=-6), A015312 (q=-7), A015313 (q=-8), A015315 (q=-9), A015316 (q=-10), A015317 (q=-11), A015319 (q=-12), A015321 (q=-13).
%K A015308 sign,easy
%O A015308 5,2
%A A015308 _Olivier Gérard_, Dec 11 1999