A037958 a(n) = binomial(n, floor((n-8)/2)).

0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 10, 11, 66, 78, 364, 455, 1820, 2380, 8568, 11628, 38760, 54264, 170544, 245157, 735471, 1081575, 3124550, 4686825, 13123110, 20030010, 54627300, 84672315, 225792840

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Links

• Robert Israel, Table of n, a(n) for n = 0..3324

Programs

GAP

List([0..40],n->Binomial(n,Int((n-8)/2))); # Muniru A Asiru, Jun 29 2018

Maple

seq(binomial(n,floor((n-8)/2)), n=0..50); # Robert Israel, Jun 28 2018

Mathematica

Table[Binomial[n,Floor[(n-8)/2]],{n,0,40}] (* Harvey P. Dale, Jun 11 2013 *)

Formula

Conjecture: -(n+9)*(n-8)*a(n) +2*(n)*a(n-1) +4*n*(n-1)*a(n-2)=0. - R. J. Mathar, Jul 26 2015, verified by Robert Israel, Jun 28 2018

From Robert Israel, Jun 28 2018: (Start)

E.g.f.: I_8(2*x)+I_9(2*x), where I_k is the modified Bessel function of the first kind and order k.

G.f.: 256*x^8/((1+sqrt(1-4*x^2))^8*sqrt(1-4*x^2)) + 512*x^9/((1+sqrt(1-4*x^2))^9*sqrt(1-4*x^2)). (End)