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A307488 G.f. A(x) satisfies: A(x) = 1 + Sum_{k>=1} mu(k)^2*x^k*A(x)^k/(1 - x^k*A(x)^k)^2, where mu() is the Möbius function (A008683). 1
1, 1, 4, 14, 59, 257, 1185, 5609, 27259, 134911, 678252, 3452924, 17767047, 92248717, 482710548, 2543031236, 13477141627, 71800541745, 384320284096, 2065782153388, 11146084675905, 60346599617759, 327749929622743, 1785153353416807, 9748766110978057, 53367282644562541 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..25.

FORMULA

G.f. A(x) satisfies: A(x) = 1 + Sum_{k>=1} psi(k)*x^k*A(x)^k, where psi() is the Dedekind psi function (A001615).

G.f.: A(x) = (1/x)*Series_Reversion(x/(1 + Sum_{k>=1} psi(k)*x^k)).

EXAMPLE

G.f.: A(x) = 1 + x + 4*x^2 + 14*x^3 + 59*x^4 + 257*x^5 + 1185*x^6 + 5609*x^7 + 27259*x^8 + 134911*x^9 + 678252*x^10 + ...

MATHEMATICA

terms = 26; CoefficientList[1/x InverseSeries[Series[x/(1 + Sum[DirichletConvolve[i, MoebiusMu[i]^2, i, k] x^k, {k, 1, terms}]), {x, 0, terms}], x], x]

terms = 26; A[_] = 0; Do[A[x_] = 1 + Sum[MoebiusMu[k]^2 x^k A[x]^k/(1 - x^k A[x]^k)^2, {k, 1, j}] + O[x]^j, {j, 1, terms}]; CoefficientList[A[x], x]

terms = 26; A[_] = 0; Do[A[x_] = 1 + Sum[DirichletConvolve[i, MoebiusMu[i]^2, i, k] x^k A[x]^k, {k, 1, j}] + O[x]^j, {j, 1, terms}]; CoefficientList[A[x], x]

CROSSREFS

Cf. A001615, A008683, A292875, A307487.

Sequence in context: A296943 A104987 A149492 * A241706 A111276 A149493

Adjacent sequences:  A307485 A307486 A307487 * A307489 A307490 A307491

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Apr 10 2019

STATUS

approved

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Last modified April 9 17:09 EDT 2020. Contains 333361 sequences. (Running on oeis4.)