A296964 Expansion of e.g.f. (exp(x)-x)*x/(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

Author

J. Devillet, Dec 22 2017

Keywords

• nonn
• easy

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

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

Crossrefs

Cf. A002627, A038156.

Programs

Mathematica

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

Sage

x = QQ[['x']].gen()
f = (exp(x) - x) * x / (1 - x)
f.egf_to_ogf()  # F. Chapoton, Jul 21 2025

Formula

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