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%I #10 Nov 01 2018 12:21:50
%S 1,1,3,7,29,71,336,932,4593,13690,69708,222718,1163734,3902016,
%T 20825927,73229397,397806717,1452193925,8016518379,30328368519,
%U 169781766056,662143701506,3755514158949,15071604241851,86496856963200,356063096545571,2066351471542036
%N a(n) = [x^n] Product_{k>=1} 1/(1 - x^k)^tau_n(k), where tau_n(k) = number of ordered n-factorizations of k.
%H Seiichi Manyama, <a href="/A321191/b321191.txt">Table of n, a(n) for n = 0..500</a>
%F a(n) = [x^n] Product_{k_1>=1, k_2>=1, ..., k_n>=1} 1/(1 - x^(k_1*k_2*...*k_n)).
%t tau[n_, 1] = 1; tau[n_, k_] := tau[n, k] = Plus @@ (tau[#, k-1] & /@ Divisors[n]); nmax = 30; Table[SeriesCoefficient[Product[1/(1 - x^k)^tau[k, n], {k, 1, n}], {x, 0, n}], {n, 0, nmax}] (* _Vaclav Kotesovec_, Oct 29 2018 *)
%Y Cf. A000041, A006171, A077592, A174465, A280487, A321192.
%K nonn
%O 0,3
%A _Ilya Gutkovskiy_, Oct 29 2018