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a(n) = Sum_{d|n} (n/d)^(d-1) * binomial(d+n-2,n-1).
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%I #12 Jul 12 2023 01:02:06

%S 1,3,7,29,71,355,925,4425,13276,60111,184757,856357,2704157,12137147,

%T 40367461,176999505,601080391,2616894901,9075135301,38884056181,

%U 138014377810,583674491643,2104098963721,8823912454489,32247616479976,133998376789707

%N a(n) = Sum_{d|n} (n/d)^(d-1) * 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/#)^(#-1) * Binomial[# + n - 2, n - 1] &]; Array[a, 25] (* _Amiram Eldar_, Jul 12 2023 *)

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

%Y Cf. A167531, A363642, A363645.

%Y Cf. A332508, A363663, A363667.

%K nonn

%O 1,2

%A _Seiichi Manyama_, Jun 14 2023