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A242428

Length of longest chain of nonempty proper subsemigroups of the dual symmetric inverse monoid.

0, 2, 17, 180, 3298, 88431, 3064050, 130905678, 6732227475, 409094032964, 28917250469178, 2346562701385648, 216180120430479731, 22397392442055209003, 2588479398843886168171, 331352273262513644199134, 46692196905193286953380160, 7203294536351261350956567853, 1210694223244114528129261255186

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OFFSET

1,2

LINKS

James Mitchell, Table of n, a(n) for n = 1..100

P. J. Cameron, M. Gadouleau, J. D. Mitchell, Y. Peresse, Chains of subsemigroups, arXiv preprint arXiv:1501.06394 [math.GR], 2015.

MATHEMATICA

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;

Array[a, 19] (* Jean-François Alcover, Dec 12 2018, from PARI *)

PROG

(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))