A050386 Exponential reversion of Moebius function A008683.

1, 1, 4, 25, 221, 2505, 34707, 568177, 10731571, 229706718, 5495040882, 145285035974, 4206973447847, 132410823640004, 4500857134998016, 164322352411837139, 6412953180173688644, 266421162165751276297

Offset: 1

Author

Christian G. Bower, Nov 15 1999

Keywords

• nonn

Links

• N. J. A. Sloane, Transforms
• Index entries for reversions of series

Crossrefs

Cf. A008683, A050385.

Programs

Mathematica

length = 40; Range[length]! InverseSeries[Sum[MoebiusMu[n] x^n/n!, {n, 1, length}] + O[x]^(length+1)][[3]] (* Vladimir Reshetnikov, Nov 07 2015 *)

PARI

seq(n)= Vec(serlaplace(serreverse(sum(k=1, n, moebius(k)*x^k/k!) + O(x*x^n)))); \\ Michel Marcus, Apr 21 2020

Formula

E.g.f. A(x) satisfies: A(x) = x - Sum_{k>=2} mu(k) * A(x)^k / k!. - Ilya Gutkovskiy, Apr 22 2020

Extensions

Typo in name corrected by Sean A. Irvine, Aug 15 2021