OFFSET
2,1
COMMENTS
a(n) represents the greatest integer solution of the (degree n polynomial) equation (k + 2*k^2 + ... + (n - 1)*k^(n - 1) + n*k^n)/(k + n) = m, where m is any positive integer.
FORMULA
a(n) = abs(Sum_{j=1..n} j*(-n)^j) - n = n*abs(((n+1)*(-n)^n+(-n)^(n+2)-1)/(n+1)^2) - n. - Giovanni Resta, May 24 2020
EXAMPLE
For n = 4, a(4) is the largest integer k > 0 such that f(k) = 4k^4 + 3k^3 + 2k^2 + k)/(k + 4) is an integer. Since f(k) is integer for k = 1, 6, 16, 39, 82, 168, 211, 426, 856, we have a(4) = 856.
MATHEMATICA
a[n_] := -n + Abs@ Sum[j (-n)^j, {j, n}]; a /@ Range[2, 19] (* Giovanni Resta, May 24 2020 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Marco Ripà, May 23 2020
EXTENSIONS
More terms from Giovanni Resta, May 24 2020
STATUS
approved