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A244491
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Number of minimal idempotent generating sets for the singular part P_n \ S_n of the partition monoid P_n.
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1
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1, 1, 3, 20, 201, 2604, 40915, 754368, 15960945, 381141008, 10139372451, 297356237760, 9530800099513, 331453265976000, 12430323314648499, 500046099516905984, 21478615942550889825, 981110493372418629888, 47489191763845877910595
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OFFSET
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0,3
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LINKS
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FORMULA
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An explicit formula is given in Th. 7.13 of East-Gray.
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MAPLE
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option remember ;
if n = 0 then
1;
elif n <=2 then
0 ;
else
(n-1)*procname(n-1)+(n-1)*(n-2)*procname(n-3) ;
end if;
end proc:
add((-1)^i*binomial(k, 2*i)*doublefactorial(2*i-1)*n^(k-2*i), i=0..floor(k/2)) ;
end proc:
end proc:
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MATHEMATICA
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a05[n_] := SeriesCoefficient[Exp[-x - x^2/2]/(1 - x), {x, 0, n}]*n!;
a90[n_, k_] := Sum[(-1)^i*Binomial[k, 2i]*(2i-1)!!*n^(k-2*i), {i, 0, k/2}];
a[n_] := Sum[Binomial[n, k]*a05[k]*a90[n, n - k], {k, 0, n}];
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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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