A334315 - OEIS

A334315

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

%I #4 Apr 22 2020 18:45:38

%S 1,-2,9,-65,653,-8432,133188,-2488450,53683569,-1313214351,

%T 35916970957,-1086055854233,35975402985863,-1295514629022924,

%U 50391598721116365,-2105485003413499952,94047072252968125326,-4472183077495496587696,225565085807090517308839

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

%C Exponential reversion of A000041 (partition numbers).

%H <a href="/index/Res#revert">Index entries for reversions of series</a>

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

%Y Cf. A000041, A007312, A050394, A066398.

%K sign

%O 1,2

%A _Ilya Gutkovskiy_, Apr 22 2020