%I #21 Aug 02 2023 02:00:40

%S 1,16,243,4112,78125,1680345,40353607,1073766400,31381060338,

%T 1000000781250,34522712143931,1283918489808640,51185893014090757,

%U 2177953338656796883,98526125335697265625,4722366482899710050304,239072435685151324847153

%N a(n) = Sum_{d|n} d^(d+n/d) * binomial(d,n/d).

%H Winston de Greef, <a href="/A360759/b360759.txt">Table of n, a(n) for n = 1..383</a>

%F G.f.: Sum_{k>0} k^k * ( (1 + k*x^k)^k - 1 ).

%F If p is prime, a(p) = p^(p+2).

%t a[n_] := DivisorSum[n, #^(# + n/#) * Binomial[#, n/#] &]; Array[a, 20] (* _Amiram Eldar_, Aug 02 2023 *)

%o (PARI) a(n) = sumdiv(n, d, d^(d+n/d)*binomial(d, n/d));

%o (PARI) my(N=20, x='x+O('x^N)); Vec(sum(k=1, N, k^k*((1+k*x^k)^k-1)))

%Y Cf. A318636, A327238, A338685, A338693, A338694.

%Y Cf. A360712.

%K nonn

%O 1,2

%A _Seiichi Manyama_, Feb 19 2023