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Search: id:A006857
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| A006857 |
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Number of permutations of n+5 which avoid the pattern 132 and have exactly 4 descents.
(Formerly M4977)
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+0
5
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| 1, 15, 105, 490, 1764, 5292, 13860, 32670, 70785, 143143, 273273, 496860, 866320, 1456560, 2372112, 3755844, 5799465, 8756055, 12954865, 18818646, 26883780, 37823500, 52474500, 71867250, 97260345, 130179231, 172459665, 226296280
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Kekule numbers for certain benzenoids. - Emeric Deutsch (deutsch(AT)duke.poly.edu), Nov 18 2005
Partial sums of A114242. - Peter Bala (pbala(AT)toucansurf.com), Sep 21 2007
Dimensions of certain Lie algebra (see reference for precise definition).
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
S. J. Cyvin and I. Gutman, Kekule structures in benzenoid hydrocarbons, Lecture Notes in Chemistry, No. 46, Springer, New York, 1988 (pp. 167-169, Table 10.5/II/1).
G. Kreweras, Traitemant simultane du "Probleme de Young" et du "Probleme de Simon Newcomb", Cahiers du Bureau Universitaire de Recherche Op\'{e}rationnelle. Institut de Statistique, Universit\'{e} de Paris, 10 (1967), 23-31.
J. M. Landsberg and L. Manivel, The sextonions and E7 1/2, Adv. Math. 201 (2006), 143-179. [Th. 7.3, case a=4]
S. Mukai, An Introduction to Invariants and Moduli, Cambridge, 2003; see p. 239.
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FORMULA
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(4+n)!*(5+n)!/(2880*n!*(n+1)!). E.g.f.: 1/2880*(2880+40320*x+109440*x^2+105120*x^3+45000*x^4+9504*x^5+1016*x^6+52*x^7+x^8)*exp(x). - Vladeta Jovovic (vladeta(AT)eunet.rs), Jan 29 2003
a(n) = C(n+4, 8)+6 C(n+5, 8)+6 C(n+6, 8)+C(n+7, 8) a(n) = C(n+3, 4)C(n+4, 4)/5 o.g.f. (1+6x+6x^2+x^3)/(1-x)^9 - Mike Zabrocki (zabrocki(AT)mathstat.yorku.ca), Aug 26 2004
a(n)=A001263(n+5,5)= binomial(n+5,5)*binomial(n+5,4)/(n+5), n>=0.
O.g.f.: (1+6*x+6*x^2+x^3)/(1-x)^9. Numerator polynomial is the fourth row polynomial of the Narayana triangle. W. Lang Nov 13 2007.
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MAPLE
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a:=n->(n+1)*(n+2)^2*(n+3)^2*(n+4)^2*(n+5)/2880: seq(a(n), n=0..38); (Deutsch)
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CROSSREFS
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Cf. A001263.
5th column of the table of Narayana numbers A001263
Cf. A114242.
Sequence in context: A010931 A076767 A022610 this_sequence A000478 A055848 A058085
Adjacent sequences: A006854 A006855 A006856 this_sequence A006858 A006859 A006860
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KEYWORD
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nonn
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AUTHOR
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Simon Plouffe (simon.plouffe(AT)gmail.com)
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EXTENSIONS
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More terms from Vladeta Jovovic (vladeta(AT)eunet.rs), Jan 29 2003
Better description from Mike Zabrocki (zabrocki(AT)mathstat.yorku.ca), Aug 26 2004
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