A301511 -id:A301511

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A308462

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

+10
2

1, 1, 4, 18, 114, 810, 7560, 71820, 822780, 10086300, 139532400, 2035618200, 33149655000, 562448086200, 10416443637600, 202624824402000, 4207527414090000, 91475485119018000, 2114681171586984000, 50821588411117524000, 1289125346347418580000

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,3

LINKS

Table of n, a(n) for n=0..20.

MATHEMATICA

nmax = 20; CoefficientList[Series[Exp[Sum[DirichletConvolve[j, MoebiusMu[j]^2, j, k] x^k/k, {k, 1, nmax}]], {x, 0, nmax}], x] Range[0, nmax]!

a[n_] := a[n] = Sum[Product[1 + Boole[PrimeQ[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. A001615, A301511, A318917.

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, May 28 2019

STATUS

approved

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