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%I A308153 #11 May 14 2019 22:05:40
%S A308153 1,1,3,7,19,47,134,357,1031,2912,8612,25007,75378,223884,683915,
%T A308153 2067578,6376800,19503546,60749341,187592661,587938043,1831377952,
%U A308153 5773159368,18092820941,57328904204,180657986051,574735018826,1820143698295,5810522774503,18473074695503
%N A308153 G.f.: x * Product_{j>=1, k>=1} 1/(1 - a(j)*x^(j*k)).
%p A308153 A:= proc(n) option remember; series(x*`if`(n=1, 1, mul(mul(
%p A308153       1/(1-a(j)*x^(j*k)), k=1..(n-1)/j), j=1..n-1)), x, n+1)
%p A308153     end:
%p A308153 a:= n-> coeff(A(n), x, n):
%p A308153 seq(a(n), n=1..35);  # _Alois P. Heinz_, May 14 2019
%t A308153 a[n_] := a[n] = SeriesCoefficient[x Product[Product[1/(1 - a[j] x^(j k)), {k, 1, n - 1}], {j, 1, n - 1}], {x, 0, n}]; Table[a[n], {n, 1, 30}]
%Y A308153 Cf. A093637, A179467, A308154.
%K A308153 nonn
%O A308153 1,3
%A A308153 _Ilya Gutkovskiy_, May 14 2019

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