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

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))

Crossrefs

Cf. A007238, A227914, A023997.

Sequence in context: A212833 A230087 A058010 * A199751 A348766 A367839

Adjacent sequences: A242425 A242426 A242427 * A242429 A242430 A242431

Keyword

nonn

Author

James Mitchell, May 14 2014

Status

approved