A003425 n! times number of posets with n elements. (Formerly M4294)

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

Offset

0,3

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

Table of n, a(n) for n=0..15.

Index entries for sequences related to posets

Formula

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

Crossrefs

Cf. A000142, A001035.

Sequence in context: A274786 A317172 A278752 * A052465 A229582 A113015

Adjacent sequences: A003422 A003423 A003424 * A003426 A003427 A003428

Keyword

nonn

Author

N. J. A. Sloane

Status

approved