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Search: id:A000565
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| A000565 |
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Number of discordant permutations.
(Formerly M5227 N2275)
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+0
3
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| 31, 696, 5823, 29380, 108933, 327840, 848380, 1958004, 4130895, 8107024, 14990889, 26372124, 44470165, 72305160, 113897310, 174496828, 260846703, 381480456, 547057075, 770735316, 1068589557, 1460069392, 1968505152, 2621661540
(list; graph; listen)
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OFFSET
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3,1
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REFERENCES
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S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures}, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
J. Riordan, Discordant permutations, Scripta Math., 20 (1954), 14-23.
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LINKS
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S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures}, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
S. Plouffe, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
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FORMULA
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G.f.: -x^7(12x^7-6x^6+88x^5-131x^4-548x^3-1123x^2-448x-31)/((1-x)^8).
a(n)=243/560n^7-243/16n^6+3591/16n^5-28737/16n^4+82257/10n^3-81931/4n^2+151931/7n, for n>6.
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MAPLE
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pp := n - >243/560*n^7 - 243/16*n^6 + 3591/16*n^5 - 28737/16*n^4 + 82257/10*n^3 - 81931/4*n^2 + 151931/7*n; seq(pp(n), n=0..30);
A000565:=-(12*z**7-6*z**6-131*z**4+88*z**5-1123*z**2-548*z**3-31-448*z)/(z-1)**8; [Conjectured by S. Plouffe in his 1992 dissertation.]
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CROSSREFS
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Sequence in context: A020983 A020981 A006097 this_sequence A014930 A061252 A096049
Adjacent sequences: A000562 A000563 A000564 this_sequence A000566 A000567 A000568
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KEYWORD
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nonn
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AUTHOR
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njas
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EXTENSIONS
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More terms, formulae and Maple code from Barbara Haas Margolius (margolius(AT)math.csuohio.edu) 2/17/01
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