A346546 E.g.f.: Product_{k>=1} 1 / (1 - x^k)^(exp(-x)/k).

1, 1, 1, 2, 15, 44, 485, 1854, 25781, 170288, 2477485, 12571140, 435748665, 2049818198, 64651106637, 628176476186, 18837010964105, 93248340364152, 6695745240354169, 33794005826851192, 2549048418922818525, 20209158430316698922, 1138228671555859916609

Offset: 0

Author

Ilya Gutkovskiy, Sep 16 2021

Keywords

• sign

Comments

Exponential transform of A002744.

The first negative term is a(37) = -2641429247236224246927617458359165366254750.

Crossrefs

Cf. A000005, A002744, A028342, A346545, A346547, A346548.

Programs

Mathematica

nmax = 22; CoefficientList[Series[Product[1/(1 - x^k)^(Exp[-x]/k), {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]!
nmax = 22; CoefficientList[Series[Exp[Exp[-x] Sum[DivisorSigma[0, k] x^k/k, {k, 1, nmax}]], {x, 0, nmax}], x] Range[0, nmax]!
A002744[n_] := Sum[(-1)^(n - k) Binomial[n, k] DivisorSigma[0, k] (k - 1)!, {k, 1, n}]; a[0] = 1; a[n_] := a[n] = Sum[Binomial[n - 1, k - 1] A002744[k] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 22}]

Formula

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

a(0) = 1; a(n) = Sum_{k=1..n} binomial(n-1,k-1) * A002744(k) * a(n-k).