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A343547 a(n) = n * Sum_{d|n} binomial(d+n-2,n-1)/d.

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%I A343547 #20 Apr 25 2021 02:22:37
%S A343547 1,4,9,32,75,318,931,3712,13014,50110,184767,715656,2704169,10454976,
%T A343547 40126395,155462016,601080407,2335849578,9075135319,35359120940,
%U A343547 137847221148,538346579034,2104098963743,8234009441952,32247603785500,126414311404108,495918587420145
%N A343547 a(n) = n * Sum_{d|n} binomial(d+n-2,n-1)/d.
%H A343547 Seiichi Manyama, <a href="/A343547/b343547.txt">Table of n, a(n) for n = 1..1000</a>
%F A343547 a(n) = [x^n] Sum_{k>=1} k * x^k/(1 - x^k)^n.
%F A343547 a(n) = [x^n] Sum_{k>=1} binomial(k+n-2,n-1) * x^k/(1 - x^k)^2.
%t A343547 a[n_] := n * DivisorSum[n, Binomial[# + n - 2, n-1]/# &]; Array[a, 30] (* _Amiram Eldar_, Apr 25 2021 *)
%o A343547 (PARI) a(n) = n*sumdiv(n, d, binomial(d+n-2, n-1)/d);
%Y A343547 Cf. A000203, A038040, A309731, A332508, A343544, A343545, A343546.
%K A343547 nonn
%O A343547 1,2
%A A343547 _Seiichi Manyama_, Apr 19 2021