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%I #5 May 15 2019 20:30:14
%S 1,1,2,8,39,240,1723,14165,130459,1331530,14894260,181259007,
%T 2383643794,33692516860,509433237073,8205927166103,140299345385359,
%U 2537807239717465,48423816128109123,972089365983087479,20481094574718083726,451904232651000126082
%N G.f.: x * Product_{k>=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 + 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. A032305, A308204, A308205, A308206.
%K nonn
%O 1,3
%A _Ilya Gutkovskiy_, May 15 2019
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