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 A005719 M2019 #37 Jul 08 2025 16:34:57 %S A005719 2,12,40,101,216,413,728,1206,1902,2882,4224,6019,8372,11403,15248, %T A005719 20060,26010,33288,42104,52689,65296,80201,97704,118130,141830,169182, %U A005719 200592,236495,277356,323671,375968,434808,500786,574532,656712,748029,849224,961077 %N A005719 Quadrinomial coefficients. %D A005719 L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 78. %D A005719 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). %H A005719 R. K. Guy, <a href="/A005712/a005712.pdf">Letter to N. J. A. Sloane, 1987</a> %H A005719 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 A005719 Simon Plouffe, <a href="/A000051/a000051_2.pdf">1031 Generating Functions</a>, Appendix to Thesis, Montreal, 1992 %F A005719 a(n)= binomial(n, 2)*(n^3+11*n^2+46*n-24)/60, n >= 2. %F A005719 G.f.: (x^2)*(2-2*x^2+x^3)/(1-x)^6. (numerator polynomial is N4(5, x) from A063421.) %F A005719 a(n) = 2*binomial(n,2) + 6*binomial(n,3) + 4*binomial(n,4) + binomial(n,5) (see comment in A071675). - _Vladimir Shevelev_ and _Peter J. C. Moses_, Jun 22 2012 %p A005719 A005719:=(2-2*z**2+z**3)/(z-1)**6; [Conjectured by _Simon Plouffe_ in his 1992 dissertation.] %Y A005719 a(n)= A008287(n, 5), n >= 2 (sixth column of quadrinomial coefficients). %K A005719 nonn %O A005719 2,1 %A A005719 _N. J. A. Sloane_