login
a(n) = Sum_{d|n} d^n * binomial(d+n/d-2, d-1).
9

%I #17 Apr 25 2021 08:51:40

%S 1,5,28,289,3126,49036,823544,17040385,387538588,10048833246,

%T 285311670612,8929334253419,302875106592254,11116754387182648,

%U 437894348359764856,18448995959423107073,827240261886336764178,39347761059781438793815,1978419655660313589123980

%N a(n) = Sum_{d|n} d^n * binomial(d+n/d-2, d-1).

%H Seiichi Manyama, <a href="/A338661/b338661.txt">Table of n, a(n) for n = 1..386</a>

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

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

%t a[n_] := DivisorSum[n, #^n * Binomial[# + n/# - 2, #-1] &]; Array[a, 20] (* _Amiram Eldar_, Apr 22 2021 *)

%o (PARI) a(n) = sumdiv(n, d, d^n*binomial(d+n/d-2, d-1));

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

%Y Cf. A023887, A157019, A157020, A324158, A324159, A339481, A339482, A339712, A343573.

%K nonn

%O 1,2

%A _Seiichi Manyama_, Apr 22 2021