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 A256031 Number of irreducible idempotents in partial Brauer monoid PB_n. 3
 2, 3, 12, 30, 240, 840, 10080, 45360, 725760, 3991680, 79833600, 518918400, 12454041600, 93405312000, 2615348736000, 22230464256000, 711374856192000, 6758061133824000, 243290200817664000, 2554547108585472000, 102181884343418880000, 1175091669949317120000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Table 2 in chapter 7 of the preprint contains a typo: a(9) is not 725860. - R. J. Mathar, Mar 14 2015 LINKS Table of n, a(n) for n=1..22. I. Dolinka, J. East, A. Evangelou, D. FitzGerald, N. Ham, J. Hyde and N. Loughlin, Enumeration of idempotents in diagram semigroups and algebras, arXiv preprint arXiv:1408.2021 [math.GR], 2014. See Prop. 22. FORMULA There are simple formulas for the two bisections - see Dolinka et al. a(2n-1) = A052612(2n-1) = A052616(2n-1) = A052849(2n-1) = A098558(2n-1) = A208529(2n+1). - Omar E. Pol, Mar 14 2015 Sum_{n>=1} 1/a(n) = (e^2+3)/(4*e) = 1/e + sinh(1)/2. - Amiram Eldar, Feb 02 2023 MAPLE A256031 := proc(n) if type(n, 'odd') then 2*n! ; else (n+1)*(n-1)! ; end if; end proc: seq(A256031(n), n=1..20) ; # R. J. Mathar, Mar 14 2015 MATHEMATICA a[n_] := If[OddQ[n], 2*n!, (n + 1)*(n - 1)!]; Array[a, 20] (* Jean-François Alcover, Nov 24 2017, from Maple *) CROSSREFS Cf. A052612, A052616, A052849, A098558, A208529, A256032, A174549 (bisection). Sequence in context: A169636 A105401 A325595 * A073617 A034381 A076424 Adjacent sequences: A256028 A256029 A256030 * A256032 A256033 A256034 KEYWORD nonn AUTHOR N. J. A. Sloane, Mar 14 2015 STATUS approved

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