proposed

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proposed

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

1, 1, 4, 14, 68, 362, 2224, 14940, 110348, 878600, 7518002, 68529122, 662709832, 6764329158, 72622813172, 817239648500, 9612724174088, 117878757097178, 1503660164683864, 19911519090176808, 273221610513382028, 3878513600608651636, 56873187579428449852, 860296560100458300892

0,3

Exponential transform of A001615.

Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/DedekindFunction.html">Dedekind Function</a>

N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>

E.g.f.: exp(Sum_{k>=1} A001615(k)*x^k/k!).

E.g.f.: A(x) = 1 + x/1! + 4*x^2/2! + 14*x^3/3! + 68*x^4/4! + 362*x^5/5! + 2224*x^6/6! + 14940*x^7/7! + ...

psi[n_] := n Sum[MoebiusMu[d]^2/d, {d, Divisors@n}]; a[n_] := a[n] = SeriesCoefficient[Exp[Sum[psi[k] x^k/k!, {k, 1, n}]], {x, 0, n}]; Table[a[n] n!, {n, 0, 23}]

psi[n_] := n Sum[MoebiusMu[d]^2/d, {d, Divisors@n}]; a[n_] := a[n] = Sum[psi[k] Binomial[n - 1, k - 1] a[n - k], {k, 1, n}]; a[0] = 1; Table[a[n], {n, 0, 23}]

Cf. A001615, A063659, A156303, A300011.

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nonn

Ilya Gutkovskiy, Mar 22 2018

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editing

allocated for Ilya Gutkovskiy

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