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A318912 Expansion of e.g.f. Product_{k>=1} 1/(1 - x^k)^(mu(k)^2/k), where mu = Möbius function (A008683). 2
1, 1, 3, 11, 53, 309, 2359, 18367, 168489, 1690217, 19416491, 233144691, 3187062493, 44901291421, 700058510943, 11509417045799, 200586478516049, 3680237286827217, 72326917665944659, 1467930587827522267, 31855597406715020421, 718484783876745110021, 16993553696264436052103 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..22.

FORMULA

E.g.f.: exp(Sum_{k>=1} 2^omega(k)*x^k/k), where omega(k) = number of distinct primes dividing k (A001221).

MAPLE

seq(n!*coeff(series(mul(1/(1-x^k)^(mobius(k)^2/k), k=1..100), x=0, 23), x, n), n=0..22); # Paolo P. Lava, Jan 09 2019

MATHEMATICA

nmax = 22; CoefficientList[Series[Product[1/(1 - x^k)^(MoebiusMu[k]^2/k), {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]!

nmax = 22; CoefficientList[Series[Exp[Sum[2^PrimeNu[k] x^k/k, {k, 1, nmax}]], {x, 0, nmax}], x] Range[0, nmax]!

a[n_] := a[n] = (n - 1)! Sum[2^PrimeNu[k] a[n - k]/(n - k)!, {k, 1, n}]; a[0] = 1; Table[a[n], {n, 0, 22}]

CROSSREFS

Cf. A001221, A008683, A028342, A034444, A073576, A206303, A318913, A318914.

Sequence in context: A005502 A305710 A000255 * A121580 A321732 A224345

Adjacent sequences:  A318909 A318910 A318911 * A318913 A318914 A318915

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Sep 05 2018

STATUS

approved

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Last modified November 11 16:05 EST 2019. Contains 329019 sequences. (Running on oeis4.)