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A086755
Sum_{k=1..n} (k(k+1))^2/2.
0
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
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
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