A037954 a(n) = binomial(n, floor((n-7)/2)).

0, 0, 0, 0, 0, 0, 0, 1, 1, 9, 10, 55, 66, 286, 364, 1365, 1820, 6188, 8568, 27132, 38760, 116280, 170544, 490314, 735471, 2042975, 3124550, 8436285, 13123110, 34597290, 54627300, 141120525, 225792840

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, A035955, A035956, A035957.

Cf. A089940, A101491.

Programs

Magma

[Binomial(n, Floor((n-7)/2)): n in [0..40]]; // G. C. Greubel, Jun 21 2022

Mathematica

Table[Binomial[n,Floor[(n-7)/2]],{n,0,40}] (* Harvey P. Dale, Apr 15 2020 *)

SageMath

[binomial(n, (n-7)//2) for n in (0..40)] # G. C. Greubel, Jun 21 2022

Formula

(n+8)*(n-7)*a(n) = 2*(n)*a(n-1) + 4*(n-1)*n*a(n-2). - R. J. Mathar, Jul 26 2015

From G. C. Greubel, Jun 21 2022: (Start)

G.f.: ((1 +x -8*x^2 -7*x^3 +20*x^4 +14*x^5 -16*x^6 -7*x^7 +2*x^8) - (1 +x -6*x^2 - 5*x^3 +10*x^4 +6*x^5 -4*x^6 -x^7)*sqrt(1-4*x^2))/(2*x^8*sqrt(1-4*x^2)).

E.g.f.: BesselI(7, 2*x) + BesselI(8, 2*x). (End)