OFFSET
1,3
LINKS
Eric Weisstein's World of Mathematics, Riemann Zeta Function
Eric Weisstein's World of Mathematics, Hurwitz Zeta Function
FORMULA
EXAMPLE
a(1) = 1^1 - 1^1 = 0;
a(2) = 1^2 - 2^1 + 2^2 - 2^2 = -1;
a(3) = 1^3 - 3^1 + 2^3 - 3^2 + 3^3 - 3^3 = -3;
a(4) = 1^4 - 4^1 + 2^4 - 4^2 + 3^4 - 4^3 + 4^4 - 4^4 = 14;
a(5) = 1^5 - 5^1 + 2^5 - 5^2 + 3^5 - 5^3 + 4^5 - 5^4 + 5^5 - 5^5 = 520, etc.
MATHEMATICA
Table[Sum[k^n - n^k, {k, 1, n}], {n, 1, 20}]
Join[{0}, Table[HarmonicNumber[n, -n] - n (n^n - 1)/(n - 1), {n, 2, 20}]]
PROG
(PARI) a(n) = sum(k=1, n, k^n - n^k); \\ Altug Alkan, Nov 23 2015
CROSSREFS
KEYWORD
sign
AUTHOR
Ilya Gutkovskiy, Nov 23 2015
STATUS
approved