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A256031
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Number of irreducible idempotents in partial Brauer monoid PB_n.
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3
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2, 3, 12, 30, 240, 840, 10080, 45360, 725760, 3991680, 79833600, 518918400, 12454041600, 93405312000, 2615348736000, 22230464256000, 711374856192000, 6758061133824000, 243290200817664000, 2554547108585472000, 102181884343418880000, 1175091669949317120000
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OFFSET
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1,1
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COMMENTS
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Table 2 in chapter 7 of the preprint contains a typo: a(9) is not 725860. - R. J. Mathar, Mar 14 2015
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LINKS
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FORMULA
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There are simple formulas for the two bisections - see Dolinka et al.
Sum_{n>=1} 1/a(n) = (e^2+3)/(4*e) = 1/e + sinh(1)/2. - Amiram Eldar, Feb 02 2023
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MAPLE
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if type(n, 'odd') then
2*n! ;
else
(n+1)*(n-1)! ;
end if;
end proc:
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MATHEMATICA
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a[n_] := If[OddQ[n], 2*n!, (n + 1)*(n - 1)!];
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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