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A301511
Expansion of e.g.f. exp(Sum_{k>=1} psi(k)*x^k/k!), where psi() is the Dedekind psi function (A001615).
1
1, 1, 4, 14, 68, 362, 2224, 14940, 110348, 878600, 7518002, 68529122, 662709832, 6764329158, 72622813172, 817239648500, 9612724174088, 117878757097178, 1503660164683864, 19911519090176808, 273221610513382028, 3878513600608651636, 56873187579428449852, 860296560100458300892
OFFSET
0,3
COMMENTS
Exponential transform of A001615.
LINKS
Eric Weisstein's World of Mathematics, Dedekind Function
N. J. A. Sloane, Transforms
FORMULA
E.g.f.: exp(Sum_{k>=1} A001615(k)*x^k/k!).
EXAMPLE
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! + ...
MATHEMATICA
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}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Mar 22 2018
STATUS
approved