A003425 n! times number of posets with n elements.

1, 1, 6, 114, 5256, 507720, 93616560, 30894489360, 17407086641280, 16152167106391680, 23990233574783750400, 55735096448700749203200, 198720975339675515386598400, 1070118060127292955589511500800, 8585695098723146508385537345689600, 101432601341702692223559539854263552000

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Comments

a(n) is the number of nonsingular elements in the semigroup B_n of all binary relations on [n]. A relation A in B_n is nonsingular iff it is regular and row rank(A) = column rank(A) = n. - Geoffrey Critzer, May 22 2022

References

• K. K.-H. Butler, A Moore-Penrose inverse for Boolean relation matrices, pp. 18-28 of Combinatorial Mathematics (Proceedings 2nd Australian Conf.), Lect. Notes Math. 403, 1974.
• K. K.-H. Butler, The Number of Partially Ordered Sets, Journal of Combinatorial Theory (B) 13, 276-289 (1972).
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• Index entries for sequences related to posets

Crossrefs

Cf. A000142, A001035.

Formula

a(n) = A000142(n) * A001035(n).