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A206810
Sum_{0<j<n} (n^4-j^4).
3
15, 145, 670, 2146, 5501, 12131, 23996, 43716, 74667, 121077, 188122, 282022, 410137, 581063, 804728, 1092488, 1457223, 1913433, 2477334, 3166954, 4002229, 5005099, 6199604, 7611980, 9270755, 11206845, 13453650, 16047150
OFFSET
2,1
COMMENTS
For a guide to related sequences, see A206817.
FORMULA
a(n) = n^5-p(n), where p(n) is the n-th partial sum of (j^4).
a(n) = t(n)-t(n-1), where t = A206811.
a(n) = (n-10*n^3-15*n^4+24*n^5)/30. G.f.: x^2*(x^3+25*x^2+55*x+15) / (x-1)^6. - Colin Barker, Jul 11 2014
EXAMPLE
a(2) = 2^4-1^4 = 15.
a(3) = (3^4-1^4) + (3^4-2^4) = 145.
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)^6 + O(x^100)) \\ Colin Barker, Jul 11 2014
(Sage) [sum([n^4-j^4 for j in range(1, n)]) for n in range(2, 30)] # Danny Rorabaugh, Apr 18 2015
CROSSREFS
Sequence in context: A026893 A368075 A163799 * A025440 A155638 A252982
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Feb 15 2012
STATUS
approved