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Expansion of e.g.f. Product_{k>=1} (1 - log(1 - x^k)).
1

%I #4 Nov 30 2019 18:34:37

%S 1,1,3,14,78,544,4560,42468,451584,5382144,69737760,985265280,

%T 15204119040,249602065920,4398839827200,82834744849920,

%U 1646970433920000,34626184595251200,769149445849989120,17896198498368583680,437123791096022016000,11171177571932111462400

%N Expansion of e.g.f. Product_{k>=1} (1 - log(1 - x^k)).

%F E.g.f.: Product_{j>=1} (1 + Sum_{i>=1} x^(i*j) / i).

%t nmax = 21; CoefficientList[Series[Product[1 - Log[1 - x^k], {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]!

%t nmax = 21; CoefficientList[Series[Product[(1 + Sum[x^(i j)/i, {i, 1, nmax}]), {j, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]!

%Y Cf. A000262, A053529, A178682.

%K nonn

%O 0,3

%A _Ilya Gutkovskiy_, Nov 30 2019