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a(n) = Sum_{d|n} d^d * binomial(d, n/d).
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%I #23 Feb 20 2023 12:25:33

%S 1,8,81,1028,15625,280017,5764801,134219264,3486784428,100000031250,

%T 3138428376721,106993206079936,3937376385699289,155568095575106627,

%U 6568408355712921875,295147905179822588160,14063084452067724991009,708235345355351624428356,37589973457545958193355601

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

%H Winston de Greef, <a href="/A338694/b338694.txt">Table of n, a(n) for n = 1..384</a>

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

%F If p is prime, a(p) = p^(p+1).

%t a[n_] := DivisorSum[n, #^# * Binomial[#, n/#] &]; Array[a, 20] (* _Amiram Eldar_, Apr 24 2021 *)

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

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

%Y Cf. A062796, A318636, A318637, A318638, A338693.

%K nonn

%O 1,2

%A _Seiichi Manyama_, Apr 24 2021