A353189 Expansion of e.g.f. exp(Sum_{k>=1} mu(k) * x^k / k), where mu() is the Moebius function (A008683).

1, 1, 0, -4, -10, -18, 112, 520, -1188, -21700, 459584, 1186704, -33320120, -917538776, 433679040, 203262002528, 3173401795088, -28004721669360, -854986923602432, -13072356448331840, -17371649304775584, 4477993621700382176, 159817807129635664640

Offset

0,4

Links

Table of n, a(n) for n=0..22.

Formula

a(0) = 1; a(n) = (n-1)! * Sum_{k=1..n} mu(k) * a(n-k)/(n-k)!.

Mathematica

a[0] = 1; a[n_] := a[n] = (n - 1)! * Sum[MoebiusMu[k] * a[n - k]/(n - k)!, {k, 1, n}]; Array[a, 23, 0] (* Amiram Eldar, Apr 30 2022 *)

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(sum(k=1, N, moebius(k)*x^k/k))))
(PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=(i-1)!*sum(j=1, i, moebius(j)*v[i-j+1]/(i-j)!)); v;

Crossrefs

Cf. A008683, A300673, A352868, A353191.

Sequence in context: A009912 A318070 A073262 * A362100 A145731 A162958

Adjacent sequences: A353186 A353187 A353188 * A353190 A353191 A353192

Keyword

sign

Author

Seiichi Manyama, Apr 29 2022

Status

approved