A004318 Binomial coefficient C(2n,n-12).

1, 26, 378, 4060, 35960, 278256, 1947792, 12620256, 76904685, 445891810, 2481256778, 13340783196, 69668534468, 354860518600, 1768966344600, 8654327655120, 41648951840265, 197548686920970, 925029565741050, 4282083008118300, 19619725782651120, 89067326568860640

Offset

12,2

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 = 12..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. - 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

E.g.f.: BesselI(12,2*x)*exp(2*x). - Ilya Gutkovskiy, Jun 28 2019

From Amiram Eldar, Aug 27 2022: (Start)

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

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

D-finite with recurrence -(n-12)*(n+12)*a(n) +2*n*(2*n-1)*a(n-1)=0. - R. J. Mathar, Jan 13 2025

Mathematica

Table[Binomial[2*n, n-12], {n, 12, 30}] (* Amiram Eldar, Aug 27 2022 *)

Prog

(PARI) a(n)=binomial(2*n, n-12) \\ Charles R Greathouse IV, Oct 23 2023

Crossrefs

Cf. A001622.

Sequence in context: A125461 A022654 A183187 * A159882 A036402 A036401

Adjacent sequences: A004315 A004316 A004317 * A004319 A004320 A004321

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved