OFFSET
2,1
COMMENTS
a(n) represents the greatest integer solution of the equation (- k + 2*k^2 - ... +/- (n - 1)*k^(n - 1) -/+ n*k^n)/(k + n) = m, where m is any integer, while a(n) is not equal to the trivial solution n + 1 (i.e., a(1) != 2 does not exist even if (- 2)/(2 - 1) = - 2).
If we introduce the additional constraint m>0, then the corresponding sequence is 8, 2, 864, ...
FORMULA
a(n) = A335112(n) + 2*n.
EXAMPLE
For n = 3, a(3) is the largest integer x > 0 such that f(k) = - 3k^3 + 2k^2 - k)/(k - 3) is an integer. Since f(k) is integer for k = 1, 2, 4, 5, 6, 9, 14, 25, 36, 69, we have a(3) = 69.
CROSSREFS
KEYWORD
nonn
AUTHOR
Marco Ripà, May 23 2020
STATUS
approved