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A306665 Expansion of Sum_{k>=0} k! * x^(k*(k+1)/2) / Product_{j=1..k} (1 - x^j)^j. 0

%I #5 Mar 04 2019 23:15:49

%S 1,1,1,3,3,7,13,19,31,57,99,145,253,391,661,1071,1647,2617,4189,6439,

%T 10183,15999,24195,37537,57553,87925,132841,202899,306147,458827,

%U 688501,1030147,1533535,2280549,3370947,4986265,7354573,10779763,15804901,23102271,33685239

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

%t nmax = 40; CoefficientList[Series[Sum[k! x^(k (k + 1)/2)/Product[(1 - x^j)^j, {j, 1, k}], {k, 0, nmax}], {x, 0, nmax}], x]

%Y Cf. A032020, A204858, A206138.

%K nonn

%O 0,4

%A _Ilya Gutkovskiy_, Mar 04 2019

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