%I #6 May 15 2019 20:29:56

%S 1,1,3,12,64,402,2972,24884,233224,2413402,27321706,335811420,

%T 4453678055,63403359154,964550068984,15618677100569,268256266076840,

%U 4871672594496080,93282009271337370,1878417037286803586,39686436905680824542,877842387051165865980

%N G.f.: x * Product_{k>=1} 1/(1 - k*x^k)^a(k).

%F Recurrence: a(n+1) = (1/n) * Sum_{k=1..n} ( Sum_{d|k} d^(k/d+1)*a(d) ) * a(n-k+1).

%t a[n_] := a[n] = SeriesCoefficient[x Product[1/(1 - k x^k)^a[k], {k, 1, n - 1}], {x, 0, n}]; Table[a[n], {n, 1, 22}]

%t a[n_] := a[n] = Sum[Sum[d^(k/d + 1) a[d], {d, Divisors[k]}] a[n - k], {k, 1, n - 1}]/(n - 1); a[1] = 1; Table[a[n], {n, 1, 22}]

%Y Cf. A000081, A308205, A308206, A308207.

%K nonn

%O 1,3

%A _Ilya Gutkovskiy_, May 15 2019