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%I #6 May 15 2019 20:30:09
%S 1,1,3,12,63,396,2926,24497,229757,2377153,26917186,330804783,
%T 4387399275,62455948949,950123048257,15384516283921,264229711285878,
%U 4798448004296966,91878671010619078,1850134691327469413,39088537892778891963,864610314507158356377
%N G.f.: x * Product_{k>=1} 1/(1 - a(k)*x^k)^k.
%F Recurrence: a(n+1) = (1/n) * Sum_{k=1..n} ( Sum_{d|k} d^2*a(d)^(k/d) ) * a(n-k+1).
%t a[n_] := a[n] = SeriesCoefficient[x Product[1/(1 - a[k] x^k)^k, {k, 1, n - 1}], {x, 0, n}]; Table[a[n], {n, 1, 22}]
%t a[n_] := a[n] = Sum[Sum[d^2 a[d]^(k/d), {d, Divisors[k]}] a[n - k], {k, 1, n - 1}]/(n - 1); a[1] = 1; Table[a[n], {n, 1, 22}]
%Y Cf. A093637, A308204, A308205, A308207.
%K nonn
%O 1,3
%A _Ilya Gutkovskiy_, May 15 2019
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