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A242428 Length of longest chain of nonempty proper subsemigroups of the dual symmetric inverse monoid. 3
0, 2, 17, 180, 3298, 88431, 3064050, 130905678, 6732227475, 409094032964, 28917250469178, 2346562701385648, 216180120430479731, 22397392442055209003, 2588479398843886168171, 331352273262513644199134, 46692196905193286953380160, 7203294536351261350956567853, 1210694223244114528129261255186 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois 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))

CROSSREFS

Cf. A007238, A227914, A023997.

Sequence in context: A212833 A230087 A058010 * A199751 A126752 A234461

Adjacent sequences:  A242425 A242426 A242427 * A242429 A242430 A242431

KEYWORD

nonn

AUTHOR

James Mitchell, May 14 2014

STATUS

approved

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Last modified October 14 01:36 EDT 2019. Contains 327994 sequences. (Running on oeis4.)