A346547 E.g.f.: Product_{k>=1} 1 / (1 - x^k)^exp(x).

1, 1, 6, 36, 282, 2575, 28075, 340809, 4657996, 69874305, 1145441713, 20279904337, 386803154474, 7874727448757, 170678885319787, 3919163707551187, 95029714996046680, 2424604353738271201, 64940619086990938317, 1820746123923294245293, 53328181409328560026038

Offset: 0

Author

Ilya Gutkovskiy, Sep 16 2021

Keywords

• nonn

Comments

Exponential transform of A002745.

Crossrefs

Cf. A000203, A002745, A053529, A346545, A346546, A346548.

Programs

Mathematica

nmax = 20; CoefficientList[Series[Product[1/(1 - x^k)^Exp[x], {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]!
nmax = 20; CoefficientList[Series[Exp[Exp[x] Sum[DivisorSigma[1, k] x^k/k, {k, 1, nmax}]], {x, 0, nmax}], x] Range[0, nmax]!
A002745[n_] := Sum[Binomial[n, k] DivisorSigma[1, k] (k - 1)!, {k, 1, n}]; a[0] = 1; a[n_] := a[n] = Sum[Binomial[n - 1, k - 1] A002745[k] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 20}]

Formula

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

a(0) = 1; a(n) = Sum_{k=1..n} binomial(n-1,k-1) * A002745(k) * a(n-k).