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a(n) = Sum_{d|n} (n/d)^n * binomial(d+n,n).
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%I #12 Jul 12 2023 01:02:13

%S 2,18,128,1590,19002,353304,6591776,154083654,3878583770,110647791078,

%T 3423740752764,116116072618104,4240251502692142,166761491097360240,

%U 7006327371058071648,313637735782416564806,14890324713956395361406,747610406539465959084870

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

%F a(n) = [x^n] Sum_{k>0} (1/(1 - (k*x)^k)^(n+1) - 1).

%t a[n_] := DivisorSum[n, (n/#)^n * Binomial[# + n, n] &]; Array[a, 20] (* _Amiram Eldar_, Jul 12 2023 *)

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

%Y Cf. A363646, A363647, A363648.

%Y Cf. A023887, A363660, A363661.

%K nonn

%O 1,1

%A _Seiichi Manyama_, Jun 14 2023