A327940 Expansion of e.g.f. exp(Sum_{i>=1} Sum_{j=1..i-1} x^(i*j) / (i*j)).

1, 0, 1, 2, 9, 44, 385, 1854, 23233, 153656, 2151441, 18787130, 338487721, 3165541092, 60609811249, 835202858294, 14913805143105, 228441779869424, 5319673396479073, 81040768940877426, 2153026504862728201, 39759334398324543260, 988919906784578473761

Offset: 0

Author

Ilya Gutkovskiy, Sep 30 2019

Keywords

• nonn

Crossrefs

Cf. A000005, A026424, A028342, A056924, A206303, A327927.

Programs

Mathematica

nmax = 22; CoefficientList[Series[Exp[Sum[Floor[DivisorSigma[0, k]/2] x^k/k, {k, 1, nmax}]], {x, 0, nmax}], x] Range[0, nmax]!
a[n_] := a[n] = If[n == 0, 1, Sum[Floor[DivisorSigma[0, k]/2] a[n - k], {k, 1, n}]/n]; Table[n! a[n], {n, 0, 22}]

Formula

E.g.f.: exp(Sum_{k>=1} floor(A000005(k)/2) * x^k / k).

E.g.f.: exp(Sum_{k>=1} A056924(k) * x^k / k).

E.g.f.: Product_{k>=1} 1 / (1 - x^A026424(k))^(1/A026424(k)).