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 A244491 Number of minimal idempotent generating sets for the singular part P_n \ S_n of the partition monoid P_n. 1
 1, 1, 3, 20, 201, 2604, 40915, 754368, 15960945, 381141008, 10139372451, 297356237760, 9530800099513, 331453265976000, 12430323314648499, 500046099516905984, 21478615942550889825, 981110493372418629888, 47489191763845877910595 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Table of n, a(n) for n=0..18. J. East, R. D. Gray, Idempotent generators in finite partition monoids and related semigroups, arXiv preprint arXiv:1404.2359 [math.GR], 2014-2016. FORMULA An explicit formula is given in Th. 7.13 of East-Gray. MAPLE A038205 := proc(n) 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: A244490 := proc(n, k) add((-1)^i*binomial(k, 2*i)*doublefactorial(2*i-1)*n^(k-2*i), i=0..floor(k/2)) ; end proc: A244491 := proc(n) add(binomial(n, k)*A038205(k)*A244490(n, n-k), k=0..n) ; end proc: seq(A244491(n), n=0..30) ; # R. J. Mathar, Aug 26 2014 MATHEMATICA 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}]; Table[a[n], {n, 0, 18}] (* Jean-François Alcover, Dec 01 2017, after R. J. Mathar *) CROSSREFS Sequence in context: A054361 A052595 A363136 * A295100 A052590 A081209 Adjacent sequences: A244488 A244489 A244490 * A244492 A244493 A244494 KEYWORD nonn AUTHOR N. J. A. Sloane, Jul 05 2014 STATUS approved

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Last modified June 10 13:58 EDT 2023. Contains 363205 sequences. (Running on oeis4.)