%I #35 Oct 23 2023 11:56:44
%S 1,24,325,3276,27405,201376,1344904,8347680,48903492,273438880,
%T 1471442973,7669339132,38910617655,192928249296,937845656300,
%U 4481381406320,21094923659355,97997533741800,449972009097765,2044802197953900,9206478467454345,41107996877935680
%N Binomial coefficient C(2n,n-11).
%D 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 Seiichi Manyama, <a href="/A004317/b004317.txt">Table of n, a(n) for n = 11..1000</a>
%H 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 Milan Janjic, <a href="https://pmf.unibl.org/wp-content/uploads/2017/10/enumfor.pdf">Two Enumerative Functions</a>
%H 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 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 -(n-11)*(n+11)*a(n) + 2*n*(2*n-1)*a(n-1) = 0. - _R. J. Mathar_, Jan 24 2018
%F E.g.f.: BesselI(11,2*x)*exp(2*x). - _Ilya Gutkovskiy_, Jun 28 2019
%F From _Amiram Eldar_, Aug 27 2022: (Start)
%F Sum_{n>=11} 1/a(n) = 338662421/23279256 - 67*Pi/(9*sqrt(3)).
%F Sum_{n>=11} (-1)^(n+1)/a(n) = 3817214*log(phi)/(5*sqrt(5)) - 1471028205721/8953560, where phi is the golden ratio (A001622). (End)
%t Table[Binomial[2n,n-11],{n,11,30}] (* _Harvey P. Dale_, Aug 02 2015 *)
%o (PARI) a(n)=binomial(2*n,n-11) \\ _Charles R Greathouse IV_, Oct 23 2023
%Y Cf. A001622.
%K nonn,easy
%O 11,2
%A _N. J. A. Sloane_