A327941 Expansion of e.g.f. exp(Sum_{i>=1} Sum_{j>=2} x^(i*j) / (i*j)).

1, 0, 1, 2, 15, 44, 595, 2274, 36673, 247400, 3660921, 29194010, 632617711, 5289743172, 117393123835, 1525153361354, 32315717350785, 433901475732944, 11698737221494513, 168831340268759730, 4894554062081828431, 87212857278031619420, 2398463635663863045411

Offset: 0

Author

Ilya Gutkovskiy, Sep 30 2019

Keywords

• nonn

Crossrefs

Cf. A000005, A028342, A032741, A206303.

Programs

Mathematica

nmax = 22; CoefficientList[Series[Exp[Sum[(DivisorSigma[0, k] - 1) x^k/k, {k, 1, nmax}]], {x, 0, nmax}], x] Range[0, nmax]!
a[n_] := a[n] = If[n == 0, 1, Sum[(DivisorSigma[0, k] - 1) a[n - k], {k, 1, n}]/n]; Table[n! a[n], {n, 0, 22}]

Formula

E.g.f.: exp(Sum_{k>=1} (A000005(k) - 1) * x^k / k).

E.g.f.: exp(Sum_{k>=1} A032741(k) * x^k / k).

E.g.f.: Product_{k>=2} 1 / (1 - x^k)^(1/k).