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Expansion of e.g.f. Product_{k>=1} 1 / (1 - mu(k)^2*x^k/k!).
1

%I #8 Mar 30 2024 02:33:05

%S 1,1,3,10,46,241,1557,11131,92212,840024,8542993,94539006,1144279566,

%T 14919897227,209774942457,3151449855040,50530826165712,

%U 859682757161697,15490902162445818,294439841770813162,5891955981426042936,123754936144549505365,2723338451934477621489

%N Expansion of e.g.f. Product_{k>=1} 1 / (1 - mu(k)^2*x^k/k!).

%F a(n) ~ c * n!, where c = Product_{k>=2} 1/(1 - mu(k)^2 / k!) = 2.424015771296779544901862396932865784522634598161012752425646675020312449... - _Vaclav Kotesovec_, Mar 28 2024

%t nmax = 22; CoefficientList[Series[Product[1/(1 - MoebiusMu[k]^2 x^k/k!), {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]!

%Y Cf. A005117, A005651, A008683, A073576, A294531, A351991, A371550.

%K nonn

%O 0,3

%A _Ilya Gutkovskiy_, Mar 27 2024