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

0,3

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).

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

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 *)

Crossrefs

Cf. A002627, A296944.

Sequence in context: A134826 A096242 A360198 * A104987 A149492 A307488

Adjacent sequences: A296940 A296941 A296942 * A296944 A296945 A296946

Keyword

nonn,easy

Author

J. Devillet, Dec 22 2017

Status

approved