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Dirichlet g.f.: 1 / zeta(s)^10.
8

%I #11 Sep 01 2021 03:09:01

%S 1,-10,-10,45,-10,100,-10,-120,45,100,-10,-450,-10,100,100,210,-10,

%T -450,-10,-450,100,100,-10,1200,45,100,-120,-450,-10,-1000,-10,-252,

%U 100,100,100,2025,-10,100,100,1200,-10,-1000,-10,-450,-450,100,-10,-2100,45,-450,100,-450

%N Dirichlet g.f.: 1 / zeta(s)^10.

%C Dirichlet inverse of A111220.

%H Seiichi Manyama, <a href="/A341836/b341836.txt">Table of n, a(n) for n = 1..10000</a>

%F Multiplicative with a(p^e) = (-1)^e * binomial(10, e).

%F a(1) = 1; a(n) = -Sum_{d|n, d < n} tau_10(n/d) * a(d).

%t a[1] = 1; a[n_] := Times @@ ((-1)^#[[2]] Binomial[10, #[[2]]] &/@ FactorInteger[n]); Table[a[n], {n, 52}]

%o (PARI) for(n=1, 100, print1(direuler(p=2, n, (1 - X)^10)[n], ", ")) \\ _Vaclav Kotesovec_, Feb 22 2021

%Y Row 10 of A346148.

%Y Cf. A007427, A007428, A008683, A111220, A247343, A341831, A341832, A341833, A341834, A341835.

%K sign,mult

%O 1,2

%A _Ilya Gutkovskiy_, Feb 21 2021