A330074 Expansion of e.g.f. Product_{k>=1} (1 - log(1 - x^k)).

1, 1, 3, 14, 78, 544, 4560, 42468, 451584, 5382144, 69737760, 985265280, 15204119040, 249602065920, 4398839827200, 82834744849920, 1646970433920000, 34626184595251200, 769149445849989120, 17896198498368583680, 437123791096022016000, 11171177571932111462400

Offset: 0

Author

Ilya Gutkovskiy, Nov 30 2019

Keywords

• nonn

Crossrefs

Cf. A000262, A053529, A178682.

Programs

Mathematica

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

Formula

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