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A003425
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n! times number of posets with n elements.
(Formerly M4294)
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3
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1, 1, 6, 114, 5256, 507720, 93616560, 30894489360, 17407086641280, 16152167106391680, 23990233574783750400, 55735096448700749203200, 198720975339675515386598400, 1070118060127292955589511500800, 8585695098723146508385537345689600, 101432601341702692223559539854263552000
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OFFSET
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0,3
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COMMENTS
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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
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REFERENCES
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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).
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LINKS
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FORMULA
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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