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%I #5 May 16 2019 21:20:17
%S 1,1,2,4,8,18,44,104,246,620,1600,4082,10436,27360,73046,193296,
%T 509984,1371214,3727792,10065872,27145058,74142688,204005440,
%U 558475342,1527058912,4213709856,11694035010,32331790700,89266126856,248240818282,693599213260
%N G.f.: x * Product_{k>=1} (1 + a(k)*(-x)^k)^((-1)^k).
%F Recurrence: a(n+1) = (1/n) * Sum_{k=1..n} ( Sum_{d|k} (-1)^(k/d+k+d+1)*d*a(d)^(k/d) ) * a(n-k+1).
%t a[n_] := a[n] = SeriesCoefficient[x Product[(1 + a[k] (-x)^k)^((-1)^k), {k, 1, n - 1}], {x, 0, n}]; Table[a[n], {n, 1, 31}]
%t a[n_] := a[n] = Sum[Sum[(-1)^(k/d + k + d + 1) d a[d]^(k/d), {d, Divisors[k]}] a[n - k], {k, 1, n - 1}]/(n - 1); a[1] = 1; Table[a[n], {n, 1, 31}]
%Y Cf. A032305, A045648, A049075, A093637, A308245.
%K nonn
%O 1,3
%A _Ilya Gutkovskiy_, May 16 2019
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