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, 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

Table of n, a(n) for n=0..23.

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

Cf. A001615, A063659, A156303, A300011.

Sequence in context: A292713 A007025 A221538 * A014512 A274804 A294222

Adjacent sequences: A301508 A301509 A301510 * A301512 A301513 A301514

Keyword

nonn

Author

Ilya Gutkovskiy, Mar 22 2018

Status

approved