A003425 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

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