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A353189
Expansion of e.g.f. exp(Sum_{k>=1} mu(k) * x^k / k), where mu() is the Moebius function (A008683).
1
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
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
KEYWORD
sign
AUTHOR
Seiichi Manyama, Apr 29 2022
STATUS
approved