A054778 5n*(5n-1)*(5n-2)*(5n-3)*(5n-4).

0, 120, 30240, 360360, 1860480, 6375600, 17100720, 38955840, 78960960, 146611080, 254251200, 417451320, 655381440, 991186560, 1452361680, 2071126800, 2884801920, 3936182040, 5273912160, 6952862280, 9034502400, 11587277520, 14686982640, 18417137760

Offset: 0

Author

Henry Bottomley, May 19 2000

Keywords

• easy
• nonn

Links

• Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).

Programs

Mathematica

With[{f=Times@@(5n-Range[0,4])},Table[f,{n,0,30}]] (* or *) LinearRecurrence[ {6,-15,20,-15,6,-1},{0,120,30240,360360,1860480,6375600},30] (* Harvey P. Dale, Aug 29 2012 *)

PARI

concat(0, Vec(120*x*(126*x^4+1246*x^3+1506*x^2+246*x+1)/(x-1)^6 + O(x^100))) \\ Colin Barker, Sep 13 2014

Formula

a(n) = A052787(5n) = 120*binomial(5*n, 5).

a(n) = 6*a(n-1)-15*a(n-2)+20*a(n-3)-15*a(n-4)+6*a(n-5)-a(n-6), with a(0)=0, a(1)=120, a(2)=30240, a(3)=360360, a(4)=1860480, a(5)=6375600. - Harvey P. Dale, Aug 29 2012

G.f.: 120*x*(126*x^4+1246*x^3+1506*x^2+246*x+1) / (x-1)^6. - Colin Barker, Sep 13 2014

Extensions

More terms from Colin Barker, Sep 13 2014