A050394 -id:A050394 - cp's OEIS frontend

A050393 Reversion of partitions into distinct parts A000009.

1, -1, 0, 3, -7, 3, 31, -105, 101, 419, -1971, 2923, 5800, -40388, 81147, 64075, -854408, 2204543, -56096, -18070916, 58866158, -38939227, -371701743, 1544696638, -1870286829, -7166094999, 39743193694, -68677654555

Offset: 1

Christian G. Bower, Nov 15 1999

sign

Vincenzo Librandi, Table of n, a(n) for n = 1..200
N. J. A. Sloane, Transforms
Index entries for reversions of series

Cf. A000009, A007312, A050394.

InverseSeries[QPochhammer[-1, x]/2 + O[x]^20][[3]] (* Vladimir Reshetnikov, Sep 22 2016 *)

G.f. A(x) satisfies: A(x) = -1 + (1 + x) * Product_{k>=2} 1/(1 + A(x)^k). - Ilya Gutkovskiy, Apr 23 2020

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

Original entry on oeis.org

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

Offset: 1

Ilya Gutkovskiy, Apr 22 2020

sign

Exponential reversion of A000041 (partition numbers).

Index entries for reversions of series

Cf. A000041, A007312, A050394, A066398.

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

cp's OEIS Frontend

A050393 Reversion of partitions into distinct parts A000009.

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