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

7,2

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, 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.

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)

Mathematica

Table[Binomial[2n, n-7], {n, 7, 30}] (* Harvey P. Dale, Nov 27 2013 *)

Prog

(Magma) [ Binomial(2*n, n-7): n in [7..150] ]; // Vincenzo Librandi, Apr 13 2011
(PARI) a(n)=binomial(2*n, n-7) \\ Charles R Greathouse IV, Oct 23 2023

Crossrefs

Diagonal 15 of triangle A100257.

Cf. A001622.

Sequence in context: A076071 A096136 A080423 * A373293 A249981 A144499

Adjacent sequences: A004310 A004311 A004312 * A004314 A004315 A004316

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved