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 A222159 T(n,k)=Number of nXk arrays with each row a permutation of 1..k having at least as many downsteps as the preceding row, with rows in lexicographically nondecreasing order 3
 1, 2, 1, 6, 3, 1, 24, 21, 4, 1, 120, 277, 56, 5, 1, 720, 6322, 2132, 126, 6, 1, 5040, 215659, 207262, 12521, 252, 7, 1, 40320, 10218797, 38778082, 4907711, 60344, 462, 8, 1, 362880, 636984802 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Table starts .1.2...6....24.....120......720.....5040.....40320.362880 .1.3..21...277....6322...215659.10218797.636984802 .1.4..56..2132..207262.38778082 .1.5.126.12521.4907711 .1.6.252.60344 .1.7.462 .1.8 .1 LINKS Table of n, a(n) for n=1..38. FORMULA Empirical for column k: k=1: a(n) = 1 k=2: a(n) = n + 1 k=3: a(n) = (1/120)*n^5 + (1/8)*n^4 + (17/24)*n^3 + (15/8)*n^2 + (137/60)*n + 1 k=4: a(n) = [polynomial degree 18] k=5: a(n) = [polynomial degree 79] EXAMPLE Some solutions for n=3 k=4 ..2..4..1..3....1..4..2..3....1..2..4..3....1..4..2..3....2..1..3..4 ..3..1..2..4....2..4..1..3....1..3..2..4....2..1..3..4....3..4..1..2 ..3..4..1..2....4..1..3..2....3..1..2..4....3..4..2..1....3..4..1..2 CROSSREFS Column 3 is A000389(n+5) Sequence in context: A221915 A249619 A345462 * A221623 A096334 A107867 Adjacent sequences: A222156 A222157 A222158 * A222160 A222161 A222162 KEYWORD nonn,tabl AUTHOR R. H. Hardin Feb 10 2013 STATUS approved

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Last modified May 30 11:09 EDT 2023. Contains 363050 sequences. (Running on oeis4.)