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.

A296943 Number of bisymmetric and quasitrivial operations on an arbitrary n-element set.

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%I A296943 #23 Jun 09 2021 14:51:25
%S A296943 0,1,4,14,58,292,1754,12280,98242,884180,8841802,97259824,1167117890,
%T A296943 15172532572,212415456010,3186231840152,50979709442434,
%U A296943 866655060521380,15599791089384842,296396030698312000,5927920613966240002,124486332893291040044
%N A296943 Number of bisymmetric and quasitrivial operations on an arbitrary n-element set.
%H A296943 Harvey P. Dale, <a href="/A296943/b296943.txt">Table of n, a(n) for n = 0..449</a>
%H A296943 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 A296943 E.g.f.: (2*exp(x)-3)/(1-x).
%F A296943 a(n+1) = (n+1)*a(n)+2, a(0)=0, a(1)=1.
%F A296943 a(n) ~ (2*exp(1) - 3) * n!. - _Vaclav Kotesovec_, Jun 05 2019
%t A296943 Join[{0}, Rest[ Range[0, 22]! CoefficientList[ Series[(2 Exp[x] -3)/(1 -x), {x, 0, 22}], x]]] (* _Robert G. Wilson v_, Dec 22 2017 *)
%t A296943 nxt[{n_,a_}]:={n+1,a(n+1)+2}; Join[{0},NestList[nxt,{1,1},20][[All,2]]] (* _Harvey P. Dale_, Jun 09 2021 *)
%Y A296943 Cf. A002627, A296944.
%K A296943 nonn,easy
%O A296943 0,3
%A A296943 _J. Devillet_, Dec 22 2017