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%I #12 May 15 2019 06:21:05
%S 1,1,2,5,11,26,64,159,397,1042,2701,7249,19341,52927,143615,399359,
%T 1099846,3087498,8616361,24386458,68617936,195678409,554862501,
%U 1590363317,4539073167,13071768304,37496646028,108449257539,312439316258,906653694239,2622887257356
%N G.f.: x * Product_{j>=1, k>=1} (1 + a(j)*x^(j*k)).
%p A:= proc(n) option remember; series(x*`if`(n=1, 1, mul(mul(
%p 1+a(j)*x^(j*k), k=1..(n-1)/j), j=1..n-1)), x, n+1)
%p end:
%p a:= n-> coeff(A(n), x, n):
%p seq(a(n), n=1..35); # _Alois P. Heinz_, May 14 2019
%t a[n_] := a[n] = SeriesCoefficient[x Product[Product[(1 + a[j] x^(j k)), {k, 1, n - 1}], {j, 1, n - 1}], {x, 0, n}]; Table[a[n], {n, 1, 32}]
%Y Cf. A032305, A308060, A308153.
%K nonn
%O 1,3
%A _Ilya Gutkovskiy_, May 14 2019