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 A360754 #13 Aug 02 2023 02:00:31 %S A360754 1,6,27,288,3125,47368,823543,16793600,387425673,10000500000, %T A360754 285311670611,8916118771200,302875106592253,11112007563452544, %U A360754 437893890412859375,18446744108073484288,827240261886336764177,39346408077084637733376 %N A360754 Expansion of Sum_{k>0} (k * x * (1 + (2 * x)^k))^k. %F A360754 a(n) = Sum_{d|n} 2^(n-d) * d^d * binomial(d,n/d-1). %F A360754 If p is an odd prime, a(p) = p^p. %t A360754 a[n_] := DivisorSum[n, 2^(n-#) * #^# * Binomial[#, n/# - 1] &]; Array[a, 20] (* _Amiram Eldar_, Aug 02 2023 *) %o A360754 (PARI) my(N=20, x='x+O('x^N)); Vec(sum(k=1, N, (k*x*(1+(2*x)^k))^k)) %o A360754 (PARI) a(n) = sumdiv(n, d, 2^(n-d)*d^d*binomial(d, n/d-1)); %Y A360754 Cf. A360732. %K A360754 nonn %O A360754 1,2 %A A360754 _Seiichi Manyama_, Feb 19 2023