A086755 Sum_{k=1..n} (k(k+1))^2/2.

2, 20, 92, 292, 742, 1624, 3192, 5784, 9834, 15884, 24596, 36764, 53326, 75376, 104176, 141168, 187986, 246468, 318668, 406868, 513590, 641608, 793960, 973960, 1185210, 1431612, 1717380, 2047052, 2425502, 2857952, 3349984, 3907552

Offset: 0

Author

Jon Perry, Jul 31 2003

Keywords

• nonn
• easy

Examples

			a(3)=(1*2)^2/2+(2*3)^2/2+(3.4)^2/2=2+18+72=92
		

Links

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

Programs

Mathematica

Table[Sum[(k(k+1))^2/2,{k,n}],{n,40}] (* or *) LinearRecurrence[{6,-15,20,-15,6,-1},{2,20,92,292,742,1624},40] (* Harvey P. Dale, Oct 04 2020 *)

PARI

for(i=1,20,print1(","sum(j=1,i,(j*(j+1))^2/2)))

Formula

(n+1)(n+2)(n+3)(3n^2+12n+10)/30 = 2*A024166(n+1).

G.f. 2*(1+4*x+x^2) / (x-1)^6 . - R. J. Mathar, Sep 15 2012

Extensions

More terms from Jason Earls, Aug 01 2003

Definition clarified by Harvey P. Dale, Oct 04 2020