A308462 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, 18, 114, 810, 7560, 71820, 822780, 10086300, 139532400, 2035618200, 33149655000, 562448086200, 10416443637600, 202624824402000, 4207527414090000, 91475485119018000, 2114681171586984000, 50821588411117524000, 1289125346347418580000

Offset

0,3

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..440

Formula

log(a(n)/n!) ~ 2*sqrt(15*n)/Pi. - Vaclav Kotesovec, Oct 31 2024

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.

Sequence in context: A326093 A222584 A294469 * A053483 A052617 A386230

Adjacent sequences: A308459 A308460 A308461 * A308463 A308464 A308465

Keyword

nonn

Author

Ilya Gutkovskiy, May 28 2019

Status

approved