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A242428
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Length of longest chain of nonempty proper subsemigroups of the dual symmetric inverse monoid.
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3
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0, 2, 17, 180, 3298, 88431, 3064050, 130905678, 6732227475, 409094032964, 28917250469178, 2346562701385648, 216180120430479731, 22397392442055209003, 2588479398843886168171, 331352273262513644199134, 46692196905193286953380160, 7203294536351261350956567853, 1210694223244114528129261255186
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OFFSET
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1,2
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LINKS
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P. J. Cameron, M. Gadouleau, J. D. Mitchell, Y. Peresse, Chains of subsemigroups, arXiv preprint arXiv:1501.06394 [math.GR], 2015.
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MATHEMATICA
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a[n_] := Sum[StirlingS2[n, i] (i! (StirlingS2[n, i] - 1)/2 - DigitCount[i, 2, 1] + Ceiling[3 i/2] + 1), {i, 1, n}] - n - 1;
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PROG
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(PARI) b(n)=if(n<1, 0, b(n\2)+n%2) /* A000120 */
a(n)=-n-1+sum(i=1, n, stirling(n, i, flag=2)*(ceil(3*i/2)-b(i)+1+(stirling(n, i, flag=2)-1)*i!/2))
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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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