cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

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%I A296964 #23 Jul 21 2025 13:57:08
%S A296964 0,1,2,9,40,205,1236,8659,69280,623529,6235300,68588311,823059744,
%T A296964 10699776685,149796873604,2246953104075,35951249665216,
%U A296964 611171244308689,11001082397556420,209020565553571999,4180411311071440000,87788637532500240021,1931350025715005280484,44421050591445121451155
%N A296964 Expansion of e.g.f. (exp(x)-x)*x/(1-x).
%C A296964 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.
%C A296964 Essentially the same as A038156. - _R. J. Mathar_, Jan 02 2018
%H A296964 J. Devillet, <a href="https://arxiv.org/abs/1712.07856">Bisymmetric and quasitrivial operations: characterizations and enumerations</a>, arXiv:1712.07856 [math.RA], 2017.
%F A296964 a(n) = A002627(n)-1, a(0)=0, a(1)=1.
%t A296964 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 *)
%o A296964 (Sage)
%o A296964 x = QQ[['x']].gen()
%o A296964 f = (exp(x) - x) * x / (1 - x)
%o A296964 f.egf_to_ogf()  # _F. Chapoton_, Jul 21 2025
%Y A296964 Cf. A002627, A038156.
%K A296964 nonn,easy
%O A296964 0,3
%A A296964 _J. Devillet_, Dec 22 2017