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Search: id:A010027
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| A010027 |
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Triangle of permutations of 1..n by number of consecutive ascending pairs. |
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+0
14
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| 1, 1, 1, 1, 2, 3, 1, 3, 9, 11, 1, 4, 18, 44, 53, 1, 5, 30, 110, 265, 309, 1, 6, 45, 220, 795, 1854, 2119, 1, 7, 63, 385, 1855, 6489, 14833, 16687, 1, 8, 84, 616, 3710, 17304, 59332, 133496, 148329, 1, 9, 108, 924, 6678, 38934, 177996, 600732, 1334961, 1468457, 1
(list; table; graph; listen)
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OFFSET
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1,5
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COMMENT
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When seen as coefficients of polynomials with decreasing exponents: evaluations are A001339 (x=2), A081923 (x=3), A081924 (x=4), A087981 (x=-1).
It appears that when x=1, P(n,x)=(n+1)! [From Timothy Hopper (timothyhopper(AT)hotmail.co.uk), Aug 20 2009]
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REFERENCES
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F. N. David, M. G. Kendall and D. E. Barton, Symmetric Function and Allied Tables, Cambridge, 1966, p. 263.
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FORMULA
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E.g.f.: exp(x*(y-1))/(1-x)^2. - Vladeta Jovovic (vladeta(AT)eunet.rs), Jan 03 2003
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EXAMPLE
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P(0,x) = 1
P(1,x) = x + 1
P(2,x) = x^2 + 2x + 3
P(3,x) = x^3 + 3x^2 + 9x + 11
P(5,x) = x^4 + 4x^3 + 18x^2 + 44x + 53
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CROSSREFS
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Cf. A000255, A000166, A000274, A000313, A001260, A001261.
Sequence in context: A134319 A135091 A111589 this_sequence A151880 A108990 A145080
Adjacent sequences: A010024 A010025 A010026 this_sequence A010028 A010029 A010030
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KEYWORD
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tabl,nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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More terms from Vladeta Jovovic (vladeta(AT)eunet.rs), Jan 03 2003
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