A204290 E.g.f. A(x) satisfies: Sum_{n>=1} moebius(n) * A(x)^n/n = x.

1, 1, 5, 35, 379, 4969, 81605, 1570715, 35014891, 882837361, 24895264085, 775645354835, 26471069590939, 981882918161209, 39334966906021925, 1692480890859290315, 77845165565219861131, 3811434080897211664321, 197923606218617044173365

Offset

1,3

Comments

Related identity: Sum_{n>=1} moebius(n)/n^s = 1/(Sum_{n>=1} 1/n^s).

Links

Table of n, a(n) for n=1..19.

Formula

E.g.f.: Series_Reversion( Sum_{n>=1} moebius(n)*x^n/n ).

Example

 E.g.f.: x + x^2/2! + 5*x^3/3! + 35*x^4/4! + 379*x^5/5! + 4969*x^6/6! +...
where the series reversion of the e.g.f. begins:
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 +...

Prog

 (PARI) {a(n)=n!*polcoeff(serreverse(sum(m=1, n, moebius(m)*x^m/m)+x*O(x^n)), n)}

Crossrefs

Sequence in context: A371028 A125864 A210996 * A059865 A247596 A325408

Adjacent sequences: A204287 A204288 A204289 * A204291 A204292 A204293

Keyword

nonn

Author

Paul D. Hanna, Jan 13 2012

Status

approved