A054778 - OEIS

%I #23 Jun 17 2017 03:53:49

%S 0,120,30240,360360,1860480,6375600,17100720,38955840,78960960,

%T 146611080,254251200,417451320,655381440,991186560,1452361680,

%U 2071126800,2884801920,3936182040,5273912160,6952862280,9034502400,11587277520,14686982640,18417137760

%N 5n*(5n-1)*(5n-2)*(5n-3)*(5n-4).

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6,-15,20,-15,6,-1).

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

%F 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

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

%t 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 *)

%o (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

%K easy,nonn

%O 0,2

%A _Henry Bottomley_, May 19 2000

%E More terms from _Colin Barker_, Sep 13 2014