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%I #22 Aug 15 2021 13:32:47
%S 1,1,4,25,221,2505,34707,568177,10731571,229706718,5495040882,
%T 145285035974,4206973447847,132410823640004,4500857134998016,
%U 164322352411837139,6412953180173688644,266421162165751276297
%N Exponential reversion of Moebius function A008683.
%H N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%H <a href="/index/Res#revert">Index entries for reversions of series</a>
%F E.g.f. A(x) satisfies: A(x) = x - Sum_{k>=2} mu(k) * A(x)^k / k!. - _Ilya Gutkovskiy_, Apr 22 2020
%t length = 40; Range[length]! InverseSeries[Sum[MoebiusMu[n] x^n/n!, {n, 1, length}] + O[x]^(length+1)][[3]] (* _Vladimir Reshetnikov_, Nov 07 2015 *)
%o (PARI) seq(n)= Vec(serlaplace(serreverse(sum(k=1, n, moebius(k)*x^k/k!) + O(x*x^n)))); \\ _Michel Marcus_, Apr 21 2020
%Y Cf. A008683, A050385.
%K nonn
%O 1,3
%A _Christian G. Bower_, Nov 15 1999
%E Typo in name corrected by _Sean A. Irvine_, Aug 15 2021