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 A006111 M5228 #42 Apr 13 2022 13:25:18
%S A006111 1,31,806,20306,508431,12714681,317886556,7947261556,198682027181,
%T A006111 4967053120931,124176340230306,3104408566792806,77610214474995931,
%U A006111 1940255363400777181,48506384092648824056,1212659602354367574056,30316490059049924214681
%N A006111 Gaussian binomial coefficient [ n,2 ] for q=5.
%D A006111 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 A006111 I. P. Goulden and D. M. Jackson, Combinatorial Enumeration. Wiley, NY, 1983, p. 99.
%D A006111 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%D A006111 M. Sved, Gaussians and binomials, Ars. Combinatoria, 17A (1984), 325-351.
%H A006111 Simon Plouffe, <a href="https://arxiv.org/abs/0911.4975">Approximations de séries génératrices et quelques conjectures</a>, Dissertation, Université du Québec à Montréal, 1992; arXiv:0911.4975 [math.NT], 2009.
%H A006111 Simon Plouffe, <a href="/A000051/a000051_2.pdf">1031 Generating Functions</a>, Appendix to Thesis, Montreal, 1992
%H A006111 M. Sved, <a href="/A006095/a006095.pdf">Gaussians and binomials</a>, Ars. Combinatoria, 17A (1984), 325-351. (Annotated scanned copy)
%H A006111 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (31,-155,125)
%F A006111 G.f.: x^2/[(1-x)(1-5x)(1-25x)].
%F A006111 a(n) = 6*a(n-1) - 5*a(n-2) + 25^(n-2), n>=4. - _Vincenzo Librandi_, Mar 20 2011
%F A006111 a(n) = 30*a(n-1) - 125*a(n-2) + 1, n>=3. - _Vincenzo Librandi_, Mar 20 2011
%F A006111 a(n) = -5^(n-1)/16 + 25^n/480 + 1/96. - _R. J. Mathar_, Mar 21 2011
%p A006111 A006111:=-1/(z-1)/(25*z-1)/(5*z-1); # [_Simon Plouffe_ in his 1992 dissertation with offset 0]
%t A006111 Transpose[NestList[Flatten[{Last[#],30Last[#]- 125First[#]+1}]&, {1,31}, 20]] [[1]] (* _Harvey P. Dale_, Mar 26 2011 *)
%t A006111 LinearRecurrence[{31, -155, 125}, {1, 31, 806}, 10] (* _T. D. Noe_, Mar 26 2011 *)
%o A006111 (Sage) [gaussian_binomial(n,2,5) for n in range(2,16)] # _Zerinvary Lajos_, May 28 2009
%K A006111 nonn
%O A006111 2,2
%A A006111 _N. J. A. Sloane_
%E A006111 More terms from _Harvey P. Dale_, Mar 26 2011