|
|
A350164
|
|
a(n) = Sum_{k=1..n}(-1)^(k+1) * floor(n/(2*k-1))^n.
|
|
2
|
|
|
1, 4, 26, 255, 3125, 46593, 823415, 16776960, 387400807, 9999941975, 285311495511, 8916083675135, 302875039491581, 11112006557122561, 437893859877597389, 18446743921164642176, 827240261123526320144, 39346407973736968327497
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
LINKS
|
|
|
FORMULA
|
a(n) = Sum_{k=1..n} Sum_{d|k} A101455(k/d) * (d^n - (d - 1)^n).
a(n) = [x^n] (1/(1 - x)) * Sum_{k>=1} (k^n - (k - 1)^n) * x^k/(1 + x^(2*k)).
|
|
MATHEMATICA
|
a[n_] := Sum[(-1)^(k + 1) * Floor[n/(2*k - 1)]^n, {k, 1, n}]; Array[a, 18] (* Amiram Eldar, Dec 18 2021 *)
|
|
PROG
|
(PARI) a(n) = sum(k=1, n, (-1)^(k+1)*(n\(2*k-1))^n);
(PARI) a(n) = sum(k=1, n, sumdiv(k, d, kronecker(-4, k/d)*(d^n-(d-1)^n)));
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|