A296943 Number of bisymmetric and quasitrivial operations on an arbitrary n-element set.
0, 1, 4, 14, 58, 292, 1754, 12280, 98242, 884180, 8841802, 97259824, 1167117890, 15172532572, 212415456010, 3186231840152, 50979709442434, 866655060521380, 15599791089384842, 296396030698312000, 5927920613966240002, 124486332893291040044
Offset: 0
Links
- Harvey P. Dale, Table of n, a(n) for n = 0..449
- J. Devillet, Bisymmetric and quasitrivial operations: characterizations and enumerations, arXiv:1712.07856 [math.RA] (2017).
Programs
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Mathematica
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 *) nxt[{n_,a_}]:={n+1,a(n+1)+2}; Join[{0},NestList[nxt,{1,1},20][[All,2]]] (* Harvey P. Dale, Jun 09 2021 *)
Formula
E.g.f.: (2*exp(x)-3)/(1-x).
a(n+1) = (n+1)*a(n)+2, a(0)=0, a(1)=1.
a(n) ~ (2*exp(1) - 3) * n!. - Vaclav Kotesovec, Jun 05 2019