login
L.g.f.: log(Sum_{k>=0} k! * x^(k*(k + 1)/2) / Product_{j=1..k} (1 - x^j)).
0

%I #4 Jan 14 2020 09:57:44

%S 1,1,7,1,11,25,15,17,-11,241,-87,217,-467,645,707,-159,35,-1451,4067,

%T -9679,17661,-19755,42413,-55615,31061,-59799,28231,147841,-230549,

%U 473185,-1013017,1656385,-2771619,3637865,-4581335,6366313,-5062635,-1059971,8699659,-22821903

%N L.g.f.: log(Sum_{k>=0} k! * x^(k*(k + 1)/2) / Product_{j=1..k} (1 - x^j)).

%F exp(Sum_{n>=1} a(n) * x^n / n) = g.f. of A032020.

%F a(n) = n * A032020(n) - Sum_{k=1..n-1} A032020(k) * a(n-k).

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

%Y Cf. A000593, A032020, A331336.

%K sign

%O 1,3

%A _Ilya Gutkovskiy_, Jan 14 2020