A308443 Expansion of e.g.f. Product_{k>=1} 1/(1 - x^k)^(psi(k)/k), where psi() is the Dedekind psi function (A001615).

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

Vaclav Kotesovec, Table of n, a(n) for n = 0..438

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

Cf. A000262, A001615, A060648, A156303.

Sequence in context: A178383 A167576 A306180 * A116151 A371651 A305127

Adjacent sequences: A308440 A308441 A308442 * A308444 A308445 A308446

Keyword

nonn

Author

Ilya Gutkovskiy, May 27 2019

Status

approved