A004313 a(n) = binomial coefficient C(2n, n-7).
1, 16, 153, 1140, 7315, 42504, 230230, 1184040, 5852925, 28048800, 131128140, 600805296, 2707475148, 12033222880, 52860229080, 229911617056, 991493848554, 4244421484512, 18053528883775, 76360380541900, 321387366339585, 1346766106565880, 5621728217559090
Offset: 7
References
- 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.
Links
- Seiichi Manyama, Table of n, a(n) for n = 7..1000
- M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
- Milan Janjic, Two Enumerative Functions
- Milan Janjic and B. Petkovic, A Counting Function, arXiv preprint arXiv:1301.4550 [math.CO], 2013. - From _N. J. A. Sloane_, Feb 13 2013
- Milan Janjic and B. Petkovic, A Counting Function Generalizing Binomial Coefficients and Some Other Classes of Integers, J. Int. Seq. 17 (2014), Article 14.3.5.
Programs
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Magma
[ Binomial(2*n,n-7): n in [7..150] ]; // Vincenzo Librandi, Apr 13 2011
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Mathematica
Table[Binomial[2n,n-7],{n,7,30}] (* Harvey P. Dale, Nov 27 2013 *) -
PARI
a(n)=binomial(2*n,n-7) \\ Charles R Greathouse IV, Oct 23 2023
Formula
-(n-7)*(n+7)*a(n) + 2*n*(2*n-1)*a(n-1) = 0. - R. J. Mathar, Jan 24 2018
E.g.f.: BesselI(7,2*x)*exp(2*x). - Ilya Gutkovskiy, Jun 27 2019
From Amiram Eldar, Aug 27 2022: (Start)
Sum_{n>=7} 1/a(n) = 41*Pi/(9*sqrt(3)) - 24923/3465.
Sum_{n>=7} (-1)^(n+1)/a(n) = 51094*log(phi)/(5*sqrt(5)) - 7616722/3465, where phi is the golden ratio (A001622). (End)