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 A004314 #49 Aug 24 2025 04:21:14
%S A004314 1,18,190,1540,10626,65780,376740,2035800,10518300,52451256,254186856,
%T A004314 1203322288,5586853480,25518731280,114955808528,511738760544,
%U A004314 2254848913647,9847379391150,42671977361650,183649923622620,785613562163430,3342649210440540,14154280149473100
%N A004314 a(n) = binomial coefficient C(2n, n - 8).
%D A004314 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 A004314 Seiichi Manyama, <a href="/A004314/b004314.txt">Table of n, a(n) for n = 8..1000</a>
%H A004314 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 A004314 Milan Janjic, <a href="https://pmf.unibl.org/wp-content/uploads/2017/10/enumfor.pdf">Two Enumerative Functions</a>
%H A004314 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 A004314 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 A004314 -(n - 8)*(n + 8)*a(n) + 2*n*(2*n - 1)*a(n - 1) = 0. - _R. J. Mathar_, Dec 10 2013
%F A004314 E.g.f.: BesselI(8,2*x) * exp(2*x). - _Ilya Gutkovskiy_, Jun 27 2019
%F A004314 From _Amiram Eldar_, Aug 27 2022: (Start)
%F A004314 Sum_{n>=8} 1/a(n) = 3941153/360360 - 49*Pi/(9*sqrt(3)).
%F A004314 Sum_{n>=8} (-1)^n/a(n) = 153506*log(phi)/(5*sqrt(5)) - 2380569277/360360, where phi is the golden ratio (A001622). (End)
%t A004314 a[n_]:=Binomial[2*n, n - 8]; Array[a, 150, 8] (* _Stefano Spezia_, Sep 01 2018 *)
%o A004314 (Magma) [Binomial(2*n, n - 8): n in [8..150] ]; // _Vincenzo Librandi_, Apr 13 2011
%o A004314 (PARI) a(n)=binomial(2*n,n-8) \\ _Charles R Greathouse IV_, Oct 23 2023
%Y A004314 Cf. A001622.
%K A004314 nonn,easy,changed
%O A004314 8,2
%A A004314 _N. J. A. Sloane_