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%I #5 Mar 06 2019 20:16:24
%S 1,1,1,1,1,2,3,1,2,5,4,7,8,5,7,11,15,22,17,31,39,20,31,39,64,81,85,
%T 125,97,170,211,121,167,229,265,385,531,548,573,814,686,1150,1339,860,
%U 1131,1344,1888,2109,2780,3656,4127,4294,4498,6320,5568,8747,10260,6856,8673,10580
%N Expansion of Sum_{k>=0} x^(k*(k+1)/2) * Product_{j=1..k} (1 + j*x^j).
%t nmax = 59; 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. A053261, A204856, A306704.
%K nonn
%O 0,6
%A _Ilya Gutkovskiy_, Mar 06 2019