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A221618 Number of n X n arrays with each row a permutation of 1..n having at least as many downsteps as the preceding row.

%I A221618 #8 Jul 23 2025 02:03:26
%S A221618 1,3,112,85035,3451956516,7575106427737240,2031241364747667201263520,
%T A221618 57096186419355436503540544000542003,
%U A221618 350680349722258761627197454626353435730368352560
%N A221618 Number of n X n arrays with each row a permutation of 1..n having at least as many downsteps as the preceding row.
%C A221618 Diagonal of A221623
%H A221618 R. H. Hardin, <a href="/A221618/b221618.txt">Table of n, a(n) for n = 1..12</a>
%e A221618 Some solutions for n=3
%e A221618 ..1..2..3....1..2..3....3..1..2....3..1..2....2..1..3....1..2..3....2..3..1
%e A221618 ..2..1..3....3..1..2....3..1..2....2..3..1....1..3..2....1..3..2....3..1..2
%e A221618 ..3..2..1....3..2..1....2..3..1....3..1..2....2..3..1....3..2..1....3..1..2
%K A221618 nonn
%O A221618 1,2
%A A221618 _R. H. Hardin_ Jan 21 2013