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Expansion of Sum_{k>=0} x^k / Product_{j=1..k} (1 + x^j)^j.
1

%I #5 Mar 05 2019 18:18:13

%S 1,1,0,1,-2,1,-2,1,-4,7,-5,7,-7,16,-13,16,-33,38,-39,31,-75,79,-92,

%T 118,-139,201,-230,269,-264,494,-476,523,-780,886,-1095,1261,-1533,

%U 1857,-2593,2197,-3367,4256,-4240,5816,-6484,7985,-9800,11051,-12561,17530,-17516

%N Expansion of Sum_{k>=0} x^k / Product_{j=1..k} (1 + x^j)^j.

%t nmax = 50; CoefficientList[Series[Sum[x^k/Product[(1 + x^j)^j, {j, 1, k}], {k, 0, nmax}], {x, 0, nmax}], x]

%Y Cf. A081362, A206100.

%K sign

%O 0,5

%A _Ilya Gutkovskiy_, Mar 05 2019