A004314 a(n) = binomial coefficient C(2n, n - 8).

1, 18, 190, 1540, 10626, 65780, 376740, 2035800, 10518300, 52451256, 254186856, 1203322288, 5586853480, 25518731280, 114955808528, 511738760544, 2254848913647, 9847379391150, 42671977361650, 183649923622620, 785613562163430, 3342649210440540, 14154280149473100

Offset

8,2

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 = 8..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.

Formula

-(n - 8)*(n + 8)*a(n) + 2*n*(2*n - 1)*a(n - 1) = 0. - R. J. Mathar, Dec 10 2013

E.g.f.: BesselI(8,2*x)*exp(2*x). - Ilya Gutkovskiy, Jun 27 2019

From Amiram Eldar, Aug 27 2022: (Start)

Sum_{n>=8} 1/a(n) = 3941153/360360 - 49*Pi/(9*sqrt(3)).

Sum_{n>=8} (-1)^n/a(n) = 153506*log(phi)/(5*sqrt(5)) - 2380569277/360360, where phi is the golden ratio (A001622). (End)

Mathematica

a[n_]:=Binomial[2*n, n - 8]; Array[a, 150, 8] (* Stefano Spezia, Sep 01 2018 *)

Prog

(Magma) [Binomial(2*n, n - 8): n in [8..150] ]; // Vincenzo Librandi, Apr 13 2011
(PARI) a(n)=binomial(2*n, n-8) \\ Charles R Greathouse IV, Oct 23 2023

Crossrefs

Cf. A001622.

Sequence in context: A022646 A268447 A259163 * A338099 A125406 A318161

Adjacent sequences: A004311 A004312 A004313 * A004315 A004316 A004317

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved