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%I #9 Sep 23 2019 14:03:53
%S 1,2,6,12,28,52,104,184,340,578,1004,1652,2752,4404,7088,11080,17362,
%T 26592,40730,61284,92096,136408,201608,294456,428952,618658,889684,
%U 1268624,1803520,2545164,3580784,5005584,6976046,9667164,13356364,18360368,25165732
%N Expansion of Product_{i>=1, j>=0} (1 + x^(i*2^j)) / (1 - x^(i*2^j)).
%C Convolution of the sequences A000041 and A092119.
%F G.f.: Product_{k>=1} ((1 + x^k) / (1 - x^k))^A001511(k).
%F G.f.: Product_{k>=1} 1 / (1 - x^k)^(A001511(k) + 1).
%t nmax = 36; CoefficientList[Series[Product[1/(1 - x^k)^(IntegerExponent[2 k, 2] + 1), {k, 1, nmax}], {x, 0, nmax}], x]
%t a[n_] := a[n] = If[n == 0, 1, Sum[Sum[d (IntegerExponent[2 d, 2] + 1), {d, Divisors[k]}] a[n - k], {k, 1, n}]/n]; Table[a[n], {n, 0, 36}]
%o (PARI) seq(n)={Vec(1/prod(k=1, n, (1 - x^k + O(x*x^n))^(2+valuation(k, 2))))} \\ _Andrew Howroyd_, Sep 23 2019
%Y Cf. A000041, A001511, A085058, A092119, A170925.
%K nonn
%O 0,2
%A _Ilya Gutkovskiy_, Sep 23 2019
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