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

Author

N. J. A. Sloane

Keywords

• nonn
• easy
• changed

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.

Crossrefs

Cf. A001622.

Programs

Mathematica

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

PARI

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

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