A037956 a(n) = binomial(n, floor((n-4)/2)).

0, 0, 0, 0, 1, 1, 6, 7, 28, 36, 120, 165, 495, 715, 2002, 3003, 8008, 12376, 31824, 50388, 125970, 203490, 497420, 817190, 1961256, 3268760, 7726160, 13037895, 30421755, 51895935, 119759850, 206253075

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, A035957.

Cf. A089940, A101491.

Programs

Magma

[Binomial(n, Floor((n-4)/2)): n in [0..40]]; // G. C. Greubel, Jun 20 2022

Maple

seq(binomial(n,floor((n-4)/2)),n=0..50); # Robert Israel, Oct 28 2019

Mathematica

Table[Binomial[n,Floor[(n-4)/2]],{n,0,40}] (* Harvey P. Dale, Mar 02 2015 *)

SageMath

[binomial(n, (n-4)//2) for n in (0..40)] # G. C. Greubel, Jun 20 2022

Formula

E.g.f.: Bessel_I(4,2x) + Bessel_I(5,2x). - Paul Barry, Feb 28 2006

(n+5)*(n-4)*a(n) = -(n^2-3*n-20)*a(n-1) - (n^2-13*n-88)*a(n-2) + 2*(2*n+3)*(n-2)*a(n-3) +20*(n-2)*(n-3)*a(n-4). - R. J. Mathar, Nov 24 2012

From Robert Israel, Oct 28 2019: (Start)

G.f.: 16*x^4*(1+2*x+sqrt(1-4*x^2))/(sqrt(1-4*x^2)*(1+sqrt(1-4*x^2))^5).

Mathar's recurrence verified using the D.E. (4*x^4-x^2)*y'' + (16*x^3+2*x^2-2*x)*y' + (8*x^2+2*x+20)*y = 0 satisfied by the G.f. (End)