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%I #10 Mar 31 2018 05:22:52
%S 1,1,3,7,12,26,52,92,170,310,541,945,1636,2760,4639,7743,12725,20795,
%T 33730,54184,86547,137351,216387,339069,528394,818664,1262245,1936835,
%U 2957432,4496330,6807191,10262275,15411203,23056461,34366753,51047199,75567600
%N Expansion of Product_{k>=1} (1 + x^k)^A034448(k).
%H Vaclav Kotesovec, <a href="/A301982/b301982.txt">Table of n, a(n) for n = 0..10000</a>
%F Conjecture: a(n) ~ exp(3 * Pi^(2/3) * n^(2/3) / 2^(5/3)) / (2^(4/3) * sqrt(3) * Pi^(1/6) * n^(2/3)).
%t nmax = 30; A034448 = Flatten[{1, Table[Times @@ (1 + Power @@@ FactorInteger[k]),{k, 2, nmax+1}]}]; CoefficientList[Series[Exp[Sum[-(-1)^j/j * Sum[A034448[[k]] * x^(j*k), {k, 1, Floor[nmax/j] + 1}], {j, 1, nmax}]], {x, 0, nmax}], x]
%Y Cf. A001615, A034448, A156303, A301594, A301981.
%K nonn
%O 0,3
%A _Vaclav Kotesovec_, Mar 30 2018
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