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 A004315 #43 Aug 24 2025 06:24:15
%S A004315 1,20,231,2024,14950,98280,593775,3365856,18156204,94143280,472733756,
%T A004315 2311801440,11058116888,51915526432,239877544005,1093260079344,
%U A004315 4923689695575,21945588357420,96926348578605,424655979547800,1847253511032930,7984465725343800,34315056105966195
%N A004315 a(n) = binomial coefficient C(2n, n-9).
%D A004315 M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 828.
%H A004315 Seiichi Manyama, <a href="/A004315/b004315.txt">Table of n, a(n) for n = 9..1000</a>
%H A004315 M. Abramowitz and I. A. Stegun, eds., <a href="http://www.convertit.com/Go/ConvertIt/Reference/AMS55.ASP">Handbook of Mathematical Functions</a>, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
%H A004315 Milan Janjic, <a href="https://pmf.unibl.org/wp-content/uploads/2017/10/enumfor.pdf">Two Enumerative Functions</a>
%H A004315 Milan Janjic and B. Petkovic, <a href="http://arxiv.org/abs/1301.4550">A Counting Function</a>, arXiv preprint arXiv:1301.4550 [math.CO], 2013. - From _N. J. A. Sloane_, Feb 13 2013
%H A004315 Milan Janjic and B. Petkovic, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL17/Janjic/janjic45.html">A Counting Function Generalizing Binomial Coefficients and Some Other Classes of Integers</a>, J. Int. Seq. 17 (2014), Article 14.3.5.
%F A004315 -(n-9)*(n+9)*a(n) + 2*n*(2*n-1)*a(n-1) = 0. - _R. J. Mathar_, Dec 10 2013
%F A004315 E.g.f.: BesselI(9,2*x) * exp(2*x). - _Ilya Gutkovskiy_, Jun 27 2019
%F A004315 From _Amiram Eldar_, Aug 27 2022: (Start)
%F A004315 Sum_{n>=9} 1/a(n) = 2*Pi/(9*sqrt(3)) + 7457/11440.
%F A004315 Sum_{n>=9} (-1)^(n+1)/a(n) = 453564*log(phi)/(5*sqrt(5)) - 14069064271/720720, where phi is the golden ratio (A001622). (End)
%t A004315 Table[Binomial[2*n, n-9], {n, 9, 30}] (* _Amiram Eldar_, Aug 27 2022 *)
%o A004315 (Magma) [ Binomial(2*n,n-9): n in [9..150] ]; // _Vincenzo Librandi_, Apr 13 2011
%o A004315 (PARI) a(n)=binomial(2*n,n-9) \\ _Charles R Greathouse IV_, Oct 23 2023
%Y A004315 Cf. A001622.
%K A004315 nonn,easy,changed
%O A004315 9,2
%A A004315 _N. J. A. Sloane_