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A206811 Sum_{0<j<k<=n} (k^4-j^4). 3
15, 160, 830, 2976, 8477, 20608, 44604, 88320, 162987, 284064, 472186, 754208, 1164345, 1745408, 2550136, 3642624, 5099847, 7013280, 9490614, 12657568, 16659797, 21664896, 27864500, 35476480, 44747235, 55954080, 69407730 (list; graph; refs; listen; history; text; internal format)
OFFSET
2,1
COMMENTS
Partial sums of A206810. For a guide to related sequences, see A206817.
LINKS
FORMULA
a(n) = (n*(1+n)^2*(1-6*n+n^2+4*n^3))/30. G.f.: -x^2*(x^3+25*x^2+55*x+15) / (x-1)^7. - Colin Barker, Jul 11 2014
EXAMPLE
a(4) = 16-1 + 81-1 + 81-16 = 160.
MATHEMATICA
s[k_] := k^4; t[1] = 0;
p[n_] := Sum[s[k], {k, 1, n}];
c[n_] := n*s[n] - p[n];
t[n_] := t[n - 1] + (n - 1) s[n] - p[n - 1]
Table[c[n], {n, 2, 50}] (* A206810 *)
Flatten[Table[t[n], {n, 2, 35}]] (* A206811 *)
PROG
(PARI) Vec(-x^2*(x^3+25*x^2+55*x+15)/(x-1)^7 + O(x^100)) \\ Colin Barker, Jul 11 2014
(Sage) [sum([sum([k^4-j^4 for j in range(1, k)]) for k in range(2, n+1)]) for n in range(2, 29)] # Danny Rorabaugh, Apr 18 2015
CROSSREFS
Sequence in context: A183555 A232415 A016297 * A027544 A021048 A095685
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Feb 15 2012
STATUS
approved

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Last modified March 28 05:39 EDT 2024. Contains 371235 sequences. (Running on oeis4.)