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Binomial coefficient C(2n,n-12).
7

%I #33 Oct 25 2023 00:19:07

%S 1,26,378,4060,35960,278256,1947792,12620256,76904685,445891810,

%T 2481256778,13340783196,69668534468,354860518600,1768966344600,

%U 8654327655120,41648951840265,197548686920970,925029565741050,4282083008118300,19619725782651120,89067326568860640

%N Binomial coefficient C(2n,n-12).

%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="/A004318/b004318.txt">Table of n, a(n) for n = 12..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 E.g.f.: BesselI(12,2*x)*exp(2*x). - _Ilya Gutkovskiy_, Jun 28 2019

%F From _Amiram Eldar_, Aug 27 2022: (Start)

%F Sum_{n>=12} 1/a(n) = 2*Pi/(9*sqrt(3)) + 29719175/46558512.

%F Sum_{n>=12} (-1)^n/a(n) = 10920956*log(phi)/(5*sqrt(5)) - 109423385475847/232792560, where phi is the golden ratio (A001622). (End)

%t Table[Binomial[2*n, n-12], {n, 12, 30}] (* _Amiram Eldar_, Aug 27 2022 *)

%o (PARI) a(n)=binomial(2*n,n-12) \\ _Charles R Greathouse IV_, Oct 23 2023

%Y Cf. A001622.

%K nonn,easy

%O 12,2

%A _N. J. A. Sloane_