A296964 Expansion of (x*exp(x)-1)/(1-x).

0, 1, 2, 9, 40, 205, 1236, 8659, 69280, 623529, 6235300, 68588311, 823059744, 10699776685, 149796873604, 2246953104075, 35951249665216, 611171244308689, 11001082397556420, 209020565553571999, 4180411311071440000, 87788637532500240021, 1931350025715005280484, 44421050591445121451155

Offset

0,3

Comments

Number of quasilinear weak orderings R on {1,...,n} and for which {1,...,n} has exactly one maximal element for the quasilinear weak ordering R.

Essentially the same as A038156. - R. J. Mathar, Jan 02 2018

Links

Table of n, a(n) for n=0..23.

J. Devillet, Bisymmetric and quasitrivial operations: characterizations and enumerations, [math.RA] arXiv:1712.07856 (2017).

Formula

a(n) = A002627(n)-1, a(0)=0, a(1)=1.

Mathematica

Join[{0, 1}, Drop[With[{nn=30}, CoefficientList[Series[(x*Exp[x]-1)/(1-x), {x, 0, nn}], x] Range[0, nn]!], 2]] (* Harvey P. Dale, Apr 02 2018 *)

Crossrefs

Cf. A002627, A038156.

Sequence in context: A052512 A166554 A038156 * A261047 A052846 A293152

Adjacent sequences: A296961 A296962 A296963 * A296965 A296966 A296967

Keyword

nonn,easy

Author

J. Devillet, Dec 22 2017

Status

approved