%I #11 Jul 12 2023 01:02:01
%S 1,3,7,37,71,751,925,13161,45676,262911,184757,18014557,2704157,
%T 133062875,2838201061,16907954129,601080391,830283170617,9075135301,
%U 87074953375981,246003195539410,53321730394923,2104098963721,479275771000215865,1952680410445479976
%N a(n) = Sum_{d|n} (n/d)^(n-n/d) * binomial(d+n-2,n-1).
%F a(n) = [x^n] Sum_{k>0} x^k/(1 - (k*x)^k)^n.
%t a[n_] := DivisorSum[n, (n/#)^(n-n/#) * Binomial[# + n - 2, n - 1] &]; Array[a, 25] (* _Amiram Eldar_, Jul 12 2023 *)
%o (PARI) a(n) = sumdiv(n, d, (n/d)^(n-n/d)*binomial(d+n-2, n-1));
%Y Cf. A342628, A359112, A363650.
%Y Cf. A363664, A363666.
%K nonn
%O 1,2
%A _Seiichi Manyama_, Jun 14 2023