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 A004316 #46 Aug 24 2025 11:34:42
%S A004316 1,22,276,2600,20475,142506,906192,5379616,30260340,163011640,
%T A004316 847660528,4280561376,21090682613,101766230790,482320623240,
%U A004316 2250829575120,10363194502115,47153358767970,212327989773900,947309492837400,4191844505805495,18412956934908690,80347448443237920
%N A004316 a(n) = binomial coefficient C(2n, n-10).
%D A004316 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 A004316 Seiichi Manyama, <a href="/A004316/b004316.txt">Table of n, a(n) for n = 10..1000</a>
%H A004316 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 A004316 Milan Janjic, <a href="https://pmf.unibl.org/wp-content/uploads/2017/10/enumfor.pdf">Two Enumerative Functions</a>
%H A004316 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 A004316 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 A004316 E.g.f.: BesselI(10,2*x) * exp(2*x). - _Ilya Gutkovskiy_, Jun 27 2019
%F A004316 From _Amiram Eldar_, Aug 27 2022: (Start)
%F A004316 Sum_{n>=10} 1/a(n) = 59*Pi/(9*sqrt(3)) - 26565167/2450448.
%F A004316 Sum_{n>=10} (-1)^n/a(n) = 1322746*log(phi)/(5*sqrt(5)) - 697534881193/12252240, where phi is the golden ratio (A001622). (End)
%F A004316 D-finite with recurrence -(n-10)*(n+10)*a(n) +2*n*(2*n-1)*a(n-1)=0. - _R. J. Mathar_, Jan 13 2025
%t A004316 Table[Binomial[2*n, n-10], {n, 10, 30}] (* _Amiram Eldar_, Aug 27 2022 *)
%o A004316 (Magma) [ Binomial(2*n,n-10): n in [10..150] ]; // _Vincenzo Librandi_, Apr 13 2011
%o A004316 (PARI) a(n)=binomial(2*n,n-10) \\ _Charles R Greathouse IV_, Oct 23 2023
%Y A004316 Cf. A001622.
%K A004316 nonn,easy,changed
%O A004316 10,2
%A A004316 _N. J. A. Sloane_