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Expansion of Sum_{k>=0} x^(k*(k+1)/2) / Product_{j=1..k} (1 + j*x^j).
1

%I #5 Mar 05 2019 18:18:19

%S 1,1,-1,2,-2,0,1,3,-5,-6,11,11,-12,-35,33,35,-22,-102,170,47,-224,

%T -491,874,695,-598,-2606,2246,1503,-664,-6420,11590,2526,-13762,

%U -34647,61785,37119,-32372,-181052,147105,104896,12824,-436333,799007,-109587,-868230,-2316921,4447531

%N Expansion of Sum_{k>=0} x^(k*(k+1)/2) / Product_{j=1..k} (1 + j*x^j).

%t nmax = 46; CoefficientList[Series[Sum[x^(k (k + 1)/2)/Product[(1 + j x^j), {j, 1, k}], {k, 0, nmax}], {x, 0, nmax}], x]

%Y Cf. A003406, A204856.

%K sign

%O 0,4

%A _Ilya Gutkovskiy_, Mar 05 2019