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%I A360712 #25 Aug 09 2023 00:52:04
%S A360712 1,5,27,272,3125,46915,823543,16781312,387421218,10000078125,
%T A360712 285311670611,8916102153177,302875106592253,11112006865911623,
%U A360712 437893890381640625,18446744074783358976,827240261886336764177,39346408075327943829273
%N A360712 Expansion of Sum_{k>0} (k * x * (1 + k*x^k))^k.
%H A360712 Seiichi Manyama, <a href="/A360712/b360712.txt">Table of n, a(n) for n = 1..386</a>
%F A360712 a(n) = Sum_{d|n} d^(d+n/d-1) * binomial(d,n/d-1).
%F A360712 If p is an odd prime, a(p) = p^p.
%t A360712 a[n_] := DivisorSum[n, #^(#+n/#-1) * Binomial[#, n/# - 1] &]; Array[a, 20] (* _Amiram Eldar_, Aug 09 2023 *)
%o A360712 (PARI) my(N=20, x='x+O('x^N)); Vec(sum(k=1, N, (k*x*(1+k*x^k))^k))
%o A360712 (PARI) a(n) = sumdiv(n, d, d^(d+n/d-1)*binomial(d, n/d-1));
%Y A360712 Cf. A217668, A327249, A338693, A359700, A360618.
%K A360712 nonn
%O A360712 1,2
%A A360712 _Seiichi Manyama_, Feb 17 2023

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