A334315 E.g.f. A(x) satisfies: A(x) = x - Sum_{k>=2} p(k) * A(x)^k / k!, where p = A000041 (partition numbers).

1, -2, 9, -65, 653, -8432, 133188, -2488450, 53683569, -1313214351, 35916970957, -1086055854233, 35975402985863, -1295514629022924, 50391598721116365, -2105485003413499952, 94047072252968125326, -4472183077495496587696, 225565085807090517308839

Offset: 1

Author

Ilya Gutkovskiy, Apr 22 2020

Keywords

• sign

Comments

Exponential reversion of A000041 (partition numbers).

Links

• Index entries for reversions of series

Crossrefs

Cf. A000041, A007312, A050394, A066398.

Programs

Mathematica

nmax = 19; CoefficientList[InverseSeries[Series[Sum[PartitionsP[k] x^k/k!, {k, 1, nmax}], {x, 0, nmax}], x], x] Range[0, nmax]! // Rest