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%I #12 Sep 01 2021 03:09:16
%S 1,-9,-9,36,-9,81,-9,-84,36,81,-9,-324,-9,81,81,126,-9,-324,-9,-324,
%T 81,81,-9,756,36,81,-84,-324,-9,-729,-9,-126,81,81,81,1296,-9,81,81,
%U 756,-9,-729,-9,-324,-324,81,-9,-1134,36,-324,81,-324,-9,756,81,756,81,81
%N Dirichlet g.f.: 1 / zeta(s)^9.
%C Dirichlet inverse of A111219.
%H Seiichi Manyama, <a href="/A341835/b341835.txt">Table of n, a(n) for n = 1..10000</a>
%F Multiplicative with a(p^e) = (-1)^e * binomial(9, e).
%F a(1) = 1; a(n) = -Sum_{d|n, d < n} tau_9(n/d) * a(d).
%t a[1] = 1; a[n_] := Times @@ ((-1)^#[[2]] Binomial[9, #[[2]]] &/@ FactorInteger[n]); Table[a[n], {n, 58}]
%o (PARI) for(n=1, 100, print1(direuler(p=2, n, (1 - X)^9)[n], ", ")) \\ _Vaclav Kotesovec_, Feb 22 2021
%Y Row 9 of A346148.
%Y Cf. A007427, A007428, A008683, A111219, A247343, A341831, A341832, A341833, A341834, A341836.
%K sign,mult
%O 1,2
%A _Ilya Gutkovskiy_, Feb 21 2021
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