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

0,1

Links

Table of n, a(n) for n=0..31.

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

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

Example

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

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 *)

Prog

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

Crossrefs

Sequence in context: A069187 A328510 A033840 * A107483 A356344 A220856

Adjacent sequences: A086752 A086753 A086754 * A086756 A086757 A086758

Keyword

nonn,easy

Author

Jon Perry, Jul 31 2003

Extensions

More terms from Jason Earls, Aug 01 2003

Definition clarified by Harvey P. Dale, Oct 04 2020

Status

approved