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Expansion of Sum_{k>0} x^k/(1 - (k*x)^k)^3.
5

%I #13 Jul 19 2023 02:19:29

%S 1,4,7,23,16,199,29,1445,4420,13271,67,751597,92,2585423,66565486,

%T 218693769,154,14527231822,191,399614708821,4080186211018,

%U 856004218103,277,2754664372347481,1430511474609701,908626846503767,900580521111136750,5626675967703843613,436

%N Expansion of Sum_{k>0} x^k/(1 - (k*x)^k)^3.

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

%t a[n_] := DivisorSum[n, (n/#)^(n-n/#) * Binomial[# + 1, 2] &]; Array[a, 30] (* _Amiram Eldar_, Jul 18 2023 *)

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

%Y Cf. A363647, A363651, A363652.

%Y Cf. A007437, A363642.

%K nonn

%O 1,2

%A _Seiichi Manyama_, Jun 13 2023