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%I #5 Mar 17 2019 21:14:21
%S 1,1,1,0,1,1,2,2,0,1,1,2,5,3,6,6,1,1,2,5,7,10,14,20,12,25,25,2,5,7,15,
%T 19,30,37,59,74,71,101,62,125,127,15,25,36,49,89,116,160,214,241,343,
%U 476,449,427,615,385,763,776,103,151,209,319,415,594,818,1068,1234,1725
%N Expansion of Sum_{k>=0} x^(k^2) * Product_{j=1..k} (1 + j*x^j).
%t nmax = 67; CoefficientList[Series[Sum[x^(k^2) Product[(1 + j x^j), {j, 1, k}], {k, 0, nmax}], {x, 0, nmax}], x]
%Y Cf. A306707, A306734, A318770.
%K nonn
%O 0,7
%A _Ilya Gutkovskiy_, Mar 16 2019