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

0,9

Links

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

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)

Mathematica

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

Prog

(Magma) [Binomial(n, Floor((n-6)/2)): n in [0..40]]; // G. C. Greubel, Jun 20 2022
(SageMath) [binomial(n, (n-6)//2) for n in (0..40)] # G. C. Greubel, Jun 20 2022
(PARI) a(n)=binomial(n, n\2-3) \\ Charles R Greathouse IV, Oct 23 2023

Crossrefs

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

Cf. A089940, A101491.

Sequence in context: A041933 A041138 A048068 * A165239 A103315 A175931

Adjacent sequences: A037954 A037955 A037956 * A037958 A037959 A037960

Keyword

nonn

Author

N. J. A. Sloane

Status

approved