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%I #12 Nov 04 2024 01:43:48
%S 1,1,5,35,379,4969,81605,1570715,35014891,882837361,24895264085,
%T 775645354835,26471069590939,981882918161209,39334966906021925,
%U 1692480890859290315,77845165565219861131,3811434080897211664321,197923606218617044173365
%N E.g.f. A(x) satisfies: Sum_{n>=1} Moebius(n) * A(x)^n/n = x.
%C Related identity: Sum_{n>=1} Moebius(n)/n^s = 1/(Sum_{n>=1} 1/n^s).
%F E.g.f.: Series_Reversion( Sum_{n>=1} Moebius(n)*x^n/n ).
%e E.g.f.: x + x^2/2! + 5*x^3/3! + 35*x^4/4! + 379*x^5/5! + 4969*x^6/6! +...
%e where the series reversion of the e.g.f. begins:
%e x - x^2/2 - x^3/3 - x^5/5 + x^6/6 - x^7/7 + x^10/10 - x^11/11 - x^13/13 + x^14/14 + x^15/15 - x^17/17 - x^19/19 + x^21/21 +...+ Moebius(n)*x^n/n +...
%o (PARI) {a(n)=n!*polcoeff(serreverse(sum(m=1,n,moebius(m)*x^m/m)+x*O(x^n)),n)}
%Y Cf. A008683.
%K nonn
%O 1,3
%A _Paul D. Hanna_, Jan 13 2012