A360824 - OEIS

%I #16 Jul 31 2023 02:25:14

%S 1,6,30,284,3130,47082,823550,16782664,387422928,10000094720,

%T 285311670622,8916102486528,302875106592266,11112006871683606,

%U 437893890382576560,18446744074918103056,827240261886336764194,39346408075331452862196

%N Expansion of Sum_{k>0} (k * x)^k / (1 - k * x^k)^(k+1).

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

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

%t a[n_] := DivisorSum[n, #^(# + n/# - 1) * Binomial[# + n/# - 1, #] &]; Array[a, 20] (* _Amiram Eldar_, Jul 31 2023 *)

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

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

%Y Cf. A339712, A343574, A360823.

%K nonn

%O 1,2

%A _Seiichi Manyama_, Feb 22 2023