A037957 a(n) = binomial(n, floor((n-6)/2)).

0, 0, 0, 0, 0, 0, 1, 1, 8, 9, 45, 55, 220, 286, 1001, 1365, 4368, 6188, 18564, 27132, 77520, 116280, 319770, 490314, 1307504, 2042975, 5311735, 8436285, 21474180, 34597290, 86493225, 141120525, 347373600

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A035951, A035952, A035953, A035954, A035955, A035956.

Cf. A089940, A101491.

Programs

Magma

[Binomial(n, Floor((n-6)/2)): n in [0..40]]; // G. C. Greubel, Jun 20 2022

Mathematica

Table[Binomial[n,Floor[(n-6)/2]],{n,0,40}] (* Harvey P. Dale, May 16 2017 *)

PARI

a(n)=binomial(n,n\2-3) \\ Charles R Greathouse IV, Oct 23 2023

SageMath

[binomial(n, (n-6)//2) for n in (0..40)] # G. C. Greubel, Jun 20 2022

Formula

(n+7)*(n-6)*a(n) = 2*n*a(n-1) + 4*n*(n-1)*a(n-2). - R. J. Mathar, Jul 26 2015

From G. C. Greubel, Jun 20 2022: (Start)

G.f.: ((1 + x - 7*x^2 - 6*x^3 + 14*x^4 + 9*x^5 - 7*x^6 - 2*x^7) - (1 + x - 5*x^2 - 4*x^3 + 6*x^4 + 3*x^5 - x^6)*sqrt(1-4*x^2))/(2*x^7*sqrt(1-4*x^2)).

E.g.f.: BesselI(6, 2*x) + BesselI(7, 2*x). (End)