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A308443
Expansion of e.g.f. Product_{k>=1} 1/(1 - x^k)^(psi(k)/k), where psi() is the Dedekind psi function (A001615).
3
1, 1, 5, 23, 173, 1249, 13249, 130255, 1670297, 21350177, 322709021, 4933457671, 87302545285, 1551234590593, 30934738239833, 630934308253439, 14035903893341489, 320008164205036225, 7885477719156600757, 198735099970790861047, 5352424525748204265821
OFFSET
0,3
LINKS
FORMULA
E.g.f.: exp(Sum_{k>=1} A060648(k)*x^k/k).
MATHEMATICA
nmax = 20; CoefficientList[Series[Product[1/(1 - x^k)^(DirichletConvolve[j, MoebiusMu[j]^2, j, k]/k), {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]!
a[n_] := a[n] = Sum[Sum[2^PrimeNu[d]/d, {d, Divisors[k]}] k! Binomial[n - 1, k - 1] a[n - k], {k, 1, n}]; a[0] = 1; Table[a[n], {n, 0, 20}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, May 27 2019
STATUS
approved