This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A350164 #19 Dec 18 2021 11:17:38 %S A350164 1,4,26,255,3125,46593,823415,16776960,387400807,9999941975, %T A350164 285311495511,8916083675135,302875039491581,11112006557122561, %U A350164 437893859877597389,18446743921164642176,827240261123526320144,39346407973736968327497 %N A350164 a(n) = Sum_{k=1..n}(-1)^(k+1) * floor(n/(2*k-1))^n. %F A350164 a(n) = Sum_{k=1..n} Sum_{d|k} A101455(k/d) * (d^n - (d - 1)^n). %F A350164 a(n) = [x^n] (1/(1 - x)) * Sum_{k>=1} (k^n - (k - 1)^n) * x^k/(1 + x^(2*k)). %F A350164 a(n) ~ n^n. - _Vaclav Kotesovec_, Dec 18 2021 %t A350164 a[n_] := Sum[(-1)^(k + 1) * Floor[n/(2*k - 1)]^n, {k, 1, n}]; Array[a, 18] (* _Amiram Eldar_, Dec 18 2021 *) %o A350164 (PARI) a(n) = sum(k=1, n, (-1)^(k+1)*(n\(2*k-1))^n); %o A350164 (PARI) a(n) = sum(k=1, n, sumdiv(k, d, kronecker(-4, k/d)*(d^n-(d-1)^n))); %Y A350164 Main diagonal of A350161. %Y A350164 Cf. A101455, A344724, A350145, A350167. %K A350164 nonn %O A350164 1,2 %A A350164 _Seiichi Manyama_, Dec 18 2021