%I #19 Apr 30 2022 12:19:22
%S 1,1,1,-2,-22,-134,-418,1044,35352,371256,2662872,2256,-348450672,
%T -7383337584,-85166363280,-224652273504,17983453809024,
%U 500248545941376,7414246148833152,13911378371907840,-2620344425592796416,-85017815816225598720,-1321651042532303189760
%N Expansion of e.g.f. 1/(1 - Sum_{k>=1} mu(k) * x^k / k), where mu() is the Moebius function (A008683).
%F a(0) = 1; a(n) = Sum_{k=1..n} (k-1)! * mu(k) * binomial(n,k) * a(n-k).
%t a[0] = 1; a[n_] := a[n] = Sum[(k - 1)! * MoebiusMu[k] * Binomial[n, k] * a[n - k], {k, 1, n}]; Array[a, 23, 0] (* _Amiram Eldar_, Apr 30 2022 *)
%o (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1-sum(k=1, N, moebius(k)*x^k/k))))
%o (PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=1, i, (j-1)!*moebius(j)*binomial(i, j)*v[i-j+1])); v;
%Y Cf. A008683, A300663, A352869, A353189.
%K sign
%O 0,4
%A _Seiichi Manyama_, Apr 29 2022