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%I #5 Jul 15 2019 15:40:31
%S 1,1,2,4,6,10,15,23,34,50,71,100,140,195,268,363,487,650,865,1145,
%T 1505,1962,2541,3275,4208,5390,6879,8740,11053,13917,17459,21837,
%U 27244,33906,42085,52085,64268,79071,97025,118772,145082,176869,215204,261333,316705,383019
%N Expansion of Product_{k>=1} (1 + (1 + x + x^2) * x^k).
%F G.f.: exp(Sum_{k>=1} x^k * Sum_{d|k} (-1)^(d+1) * (1 + x + x^2)^d/d).
%t nmax = 45; CoefficientList[Series[Product[(1 + (1 + x + x^2) x^k), {k, 1, nmax}], {x, 0, nmax}], x]
%t nmax = 45; CoefficientList[Series[Exp[Sum[x^k Sum[(-1)^(d + 1) (1 + x + x^2)^d/d, {d, Divisors[k]}], {k, 1, nmax}]], {x, 0, nmax}], x]
%Y Cf. A160571, A227681, A309172.
%K nonn
%O 0,3
%A _Ilya Gutkovskiy_, Jul 15 2019
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