|
%I M4294 #19 May 22 2022 16:21:07
%S 1,1,6,114,5256,507720,93616560,30894489360,17407086641280,
%T 16152167106391680,23990233574783750400,55735096448700749203200,
%U 198720975339675515386598400,1070118060127292955589511500800,8585695098723146508385537345689600,101432601341702692223559539854263552000
%N n! times number of posets with n elements.
%C 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
%D 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.
%D K. K.-H. Butler, The Number of Partially Ordered Sets, Journal of Combinatorial Theory (B) 13, 276-289 (1972).
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H <a href="/index/Pos#posets">Index entries for sequences related to posets</a>
%F a(n) = A000142(n) * A001035(n).
%Y Cf. A000142, A001035.
%K nonn
%O 0,3
%A _N. J. A. Sloane_
|
