%I #15 Dec 17 2021 10:44:36
%S 1,4,28,257,3127,46721,823673,16777474,387440175,10000060075,
%T 285311849809,8916117229571,302875173709313,11112007094026243,
%U 437893920912819179,18446744226340554502,827240262649405488542,39346408176856882188621
%N a(n) = Sum_{k=1..n} floor(n/(2*k-1))^n.
%F a(n) = Sum_{k=1..n} Sum_{d|k, k/d odd} d^n - (d - 1)^n.
%F a(n) = [x^n] (1/(1 - x)) * Sum_{k>=1} (k^n - (k - 1)^n) * x^k/(1 - x^(2*k)).
%F a(n) ~ n^n. - _Vaclav Kotesovec_, Dec 17 2021
%t a[n_] := Sum[Floor[n/(2*k - 1)]^n, {k, 1, n}]; Array[a, 20] (* _Amiram Eldar_, Dec 17 2021 *)
%o (PARI) a(n) = sum(k=1, n, (n\(2*k-1))^n);
%o (PARI) a(n) = sum(k=1, n, sumdiv(k, d, k/d%2*(d^n-(d-1)^n)));
%Y Main diagonal of A350122.
%Y Cf. A350147.
%K nonn
%O 1,2
%A _Seiichi Manyama_, Dec 16 2021