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A306483 Expansion of Product_{k>=1} 1/(1 - psi(k)*x^k), where psi() is the Dedekind psi function (A001615). 1
1, 1, 4, 8, 23, 41, 114, 200, 491, 909, 2036, 3710, 8235, 14743, 31058, 56538, 115435, 207401, 417876, 745578, 1470371, 2626489, 5086108, 9030162, 17347019, 30620651, 58060380, 102426652, 192288399, 337633825, 629845430, 1101958752, 2040109199, 3563507377, 6553539316, 11412799294 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Vaclav Kotesovec, Table of n, a(n) for n = 0..1000

FORMULA

G.f.: exp(Sum_{k>=1} Sum_{j>=1} psi(j)^k*x^(j*k)/k).

From Vaclav Kotesovec, Feb 23 2019: (Start)

a(n) ~ c * 3^(n/2), where

c = 84.0923381459819921541124348082985... if n is even and

c = 82.6952907990079575265849718772977... if n is odd. (End)

MATHEMATICA

nmax = 35; CoefficientList[Series[Product[1/(1 - DirichletConvolve[i, MoebiusMu[i]^2, i, k] x^k), {k, 1, nmax}], {x, 0, nmax}], x]

nmax = 35; CoefficientList[Series[Exp[Sum[Sum[DirichletConvolve[i, MoebiusMu[i]^2, i, j]^k x^(j k)/k, {j, 1, nmax}], {k, 1, nmax}]], {x, 0, nmax}], x]

a[n_] := a[n] = If[n == 0, 1, Sum[Sum[d DirichletConvolve[i, MoebiusMu[i]^2, i, d]^(k/d), {d, Divisors[k]}] a[n - k], {k, 1, n}]/n]; Table[a[n], {n, 0, 35}]

CROSSREFS

Cf. A001615, A156303, A319111.

Sequence in context: A075688 A272563 A272152 * A274521 A026596 A181688

Adjacent sequences:  A306480 A306481 A306482 * A306484 A306485 A306486

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Feb 18 2019

STATUS

approved

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Last modified September 20 12:43 EDT 2019. Contains 327238 sequences. (Running on oeis4.)