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 A004318 #40 Aug 24 2025 04:20:36
%S A004318 1,26,378,4060,35960,278256,1947792,12620256,76904685,445891810,
%T A004318 2481256778,13340783196,69668534468,354860518600,1768966344600,
%U A004318 8654327655120,41648951840265,197548686920970,925029565741050,4282083008118300,19619725782651120,89067326568860640
%N A004318 Binomial coefficient C(2n,n-12).
%D A004318 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 A004318 Seiichi Manyama, <a href="/A004318/b004318.txt">Table of n, a(n) for n = 12..1000</a>
%H A004318 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 A004318 Milan Janjic, <a href="https://pmf.unibl.org/wp-content/uploads/2017/10/enumfor.pdf">Two Enumerative Functions</a>.
%H A004318 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. - _N. J. A. Sloane_, Feb 13 2013
%H A004318 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 A004318 E.g.f.: BesselI(12,2*x) * exp(2*x). - _Ilya Gutkovskiy_, Jun 28 2019
%F A004318 From _Amiram Eldar_, Aug 27 2022: (Start)
%F A004318 Sum_{n>=12} 1/a(n) = 2*Pi/(9*sqrt(3)) + 29719175/46558512.
%F A004318 Sum_{n>=12} (-1)^n/a(n) = 10920956*log(phi)/(5*sqrt(5)) - 109423385475847/232792560, where phi is the golden ratio (A001622). (End)
%F A004318 D-finite with recurrence -(n-12)*(n+12)*a(n) +2*n*(2*n-1)*a(n-1)=0. - _R. J. Mathar_, Jan 13 2025
%t A004318 Table[Binomial[2*n, n-12], {n, 12, 30}] (* _Amiram Eldar_, Aug 27 2022 *)
%o A004318 (PARI) a(n)=binomial(2*n,n-12) \\ _Charles R Greathouse IV_, Oct 23 2023
%Y A004318 Cf. A001622.
%K A004318 nonn,easy,changed
%O A004318 12,2
%A A004318 _N. J. A. Sloane_