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%I #41 Jun 19 2021 04:58:05
%S 1,2,8,29,118,427,1671,6260,24034,91301,351261,1345434,5191170,
%T 20018845,77500485,300290041,1166450850,4535971707,17670369300,
%U 68913194733,269114332057,1051984590581,4116622325140,16123381985750,63204699026898,247956554702702
%N Number of ordered n-tuples of integers from [ 1..n ] with no global factor.
%H Seiichi Manyama, <a href="/A345131/b345131.txt">Table of n, a(n) for n = 1..1000</a>
%F a(n) = Sum_{k=1..n} Sum_{d|k} mu(k/d) * binomial(d+n-2, d-1).
%F a(n) = [x^n] (1/(1 - x)) * Sum_{k>=1} mu(k) * x^k / (1 - x^k)^n.
%F a(n) ~ 2^(2*n-1) / sqrt(Pi*n). - _Vaclav Kotesovec_, Jun 19 2021
%t a[n_] := Sum[DivisorSum[k, MoebiusMu[k/#] * Binomial[n + # - 2, # - 1] &], {k, 1, n}]; Array[a, 25] (* _Amiram Eldar_, Jun 13 2021 *)
%o (PARI) a(n) = sum(k=1, n, sumdiv(k, d, moebius(k/d)*binomial(d+n-2, d-1)));
%Y Main diagonal of A177976.
%Y Cf. A332470.
%K nonn
%O 1,2
%A _Seiichi Manyama_, Jun 12 2021
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