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%I #5 Mar 04 2019 23:15:40
%S 1,0,1,1,1,1,2,2,4,4,7,7,12,12,19,22,31,37,54,63,89,111,146,184,247,
%T 301,398,501,642,804,1042,1293,1663,2082,2648,3321,4229,5268,6691,
%U 8370,10553,13168,16595,20659,25929,32253,40321,50092,62489,77418,96340,119266,147998,182927,226609
%N Expansion of Sum_{k>=0} x^(k*(k+1)) / Product_{j=1..k} (1 - x^j)^j.
%t nmax = 54; CoefficientList[Series[Sum[x^(k (k + 1))/Product[(1 - x^j)^j, {j, 1, k}], {k, 0, nmax}], {x, 0, nmax}], x]
%Y Cf. A003106, A206100, A206138.
%K nonn
%O 0,7
%A _Ilya Gutkovskiy_, Mar 04 2019