A291288 a(n) = binomial(n+3, 3)*(1 + binomial(n+2, 3)/4).

1, 5, 20, 70, 210, 546, 1260, 2640, 5115, 9295, 16016, 26390, 41860, 64260, 95880, 139536, 198645, 277305, 380380, 513590, 683606, 898150, 1166100, 1497600, 1904175, 2398851, 2996280, 3712870, 4566920, 5578760, 6770896, 8168160, 9797865, 11689965

Offset: 0

Author

N. J. A. Sloane, Aug 28 2017

Keywords

• nonn

Links

• Robert Israel, Table of n, a(n) for n = 0..10000
• Isaac Ahern, Sam Cook, Affine Symmetry Tensors in Minkowski Space, American Journal of Undergraduate Research, Volume 13 | Issue 3 | August 2016.
• Index entries for linear recurrences with constant coefficients, signature (7, -21, 35, -35, 21, -7, 1).

Programs

Maple

f:=n->binomial(n+3,3)*(1+binomial(n+2,3)/4);
[seq(f(n),n=0..40)];

Mathematica

Table[Binomial[n+3,3](1+Binomial[n+2,3]/4),{n,0,40}] (* or *) LinearRecurrence[{7,-21,35,-35,21,-7,1},{1,5,20,70,210,546,1260},40] (* Harvey P. Dale, Mar 12 2024 *)

Formula

From Robert Israel, Aug 28 2017: (Start)

a(n) = (n+1)*(n+2)*(n+3)*(n+4)*(n^2-n+6)/144.

n*a(n) - (2+3*n)*a(n-1) + (8*n-16)*a(n-2) - (12+6*n)*a(n-3) = 0.

G.f.: (6*x^2-2*x+1)/(1-x)^7. (End)