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%I #6 May 15 2019 20:30:03
%S 1,1,2,8,38,234,1679,13802,127155,1297619,14516296,176640311,
%T 2322876382,32831464503,496399943530,7995690518504,136701790293581,
%U 2472679442088700,47180405307783443,947116124382018095,19954735355719570880,440286840550877179031
%N G.f.: x * Product_{k>=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 + 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. A004111, A308204, A308206, A308207.
%K nonn
%O 1,3
%A _Ilya Gutkovskiy_, May 15 2019
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