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A152457 Partial sums of A027444. 0
0, 3, 17, 56, 140, 295, 553, 952, 1536, 2355, 3465, 4928, 6812, 9191, 12145, 15760, 20128, 25347, 31521, 38760, 47180, 56903, 68057, 80776, 95200, 111475, 129753, 150192, 172956, 198215, 226145, 256928, 290752, 327811, 368305, 412440, 460428 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

1^1+1^2+1^3=3; (2^1+2^2+2^3)+3=17; ...

LINKS

Table of n, a(n) for n=0..36.

Index entries for linear recurrences with constant coefficients, signature (5, -10, 10, -5, 1).

FORMULA

a(n) = n(n + 1)(3n^2 + 7n + 8)/12. - Giovanni Resta, Jun 15 2013

a(0)=0, a(1)=3, a(2)=17, a(3)=56, a(4)=140, a(n)=5*a(n-1)-10*a(n-2)+ 10*a(n-3)- 5*a(n-4)+a(n-5). - Harvey P. Dale, Dec 13 2013

G.f.: -x*(3+2*x+x^2) / (x-1)^5 . - R. J. Mathar, Jul 18 2016

MATHEMATICA

Table[Sum[i + i^2 + i^3, {i, n}], {n, 0, 25}]

Accumulate[Table[n^3+n^2+n, {n, 0, 50}]] (* or *) LinearRecurrence[ {5, -10, 10, -5, 1}, {0, 3, 17, 56, 140}, 50] (* Harvey P. Dale, Dec 13 2013 *)

CROSSREFS

Sequence in context: A258032 A033562 A212415 * A130857 A226719 A168547

Adjacent sequences:  A152454 A152455 A152456 * A152458 A152459 A152460

KEYWORD

nonn

AUTHOR

Vladimir Joseph Stephan Orlovsky, Dec 05 2008

EXTENSIONS

Definition corrected by Jeremy Gardiner, Jun 15 2013

STATUS

approved

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Last modified February 22 09:43 EST 2019. Contains 320390 sequences. (Running on oeis4.)