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Search: id:A138163
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| A138163 |
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Number of permutations of {1,2,...,n} containing exactly 5 occurrences of the pattern 132. |
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3
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| 5, 55, 394, 2225, 11539, 57064, 273612, 1283621, 5924924, 27005978, 121861262, 545368160, 2423923480, 10710273856, 47085144255, 206085075295, 898489543020, 3903621095130, 16906888008960, 73018012573950, 314540265217362
(list; graph; listen)
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OFFSET
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5,1
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COMMENT
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a(n)=A138160(n,5).
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REFERENCES
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M. Bona, Permutations with one or two 132-subsequences, Discrete Math., 181, 1998, 267-274.
M. Bona, The number of permutations with exactly r 132-subsequences is P-recursive in the size, Adv. Appl. Math., 18, 1997, 510-522.
T. Mansour and A. Vainshtein, Counting occurrences of 132 in a permutation
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FORMULA
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a(n)=(n^12+170n^11+1861n^10-88090n^9-307617n^8+27882510n^7-348117457n^6+2119611370n^5-6970280884n^4+10530947320n^3+2614396896n^2-30327454080n+29059430400)(2n-15)!/[120 n!(n-7)! ] for n>=8; a(5)=5; a(6)=55; a(7)=394. G.f.=(1/2)[P(x) + Q(x)/(1-4x)^(9/2)], where P(x)=14x^5-17x^4+x^3-16x^2+14x-2, Q(x)=-50x^11-2568x^10-10826x^9+16252x^8-12466x^7+16184x^6-16480x^5+9191x^4- 2893x^3+520x^2-50x+2.
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EXAMPLE
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a(5)=5 because we have 13542, 14532, 15243, 15342, and 15423.
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MAPLE
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a:=proc(n) options operator, arrow: (1/120)*(n^12+170*n^11+1861*n^10-88090*n^9-307617*n^8+27882510*n^7-348117457*n^6+2119611370*n^5-6970280884*n^4+10530947320*n^3+2614396896*n^2-30327454080*n+29059430400)*factorial(2*n-15)/(factorial(n)*factorial(n-7)) end proc: 5, 55, 394, seq(a(n), n = 8 .. 25);
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CROSSREFS
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Cf. A002054, A082970, A082971, A138162, A138160.
Adjacent sequences: A138160 A138161 A138162 this_sequence A138164 A138165 A138166
Sequence in context: A060558 A014852 A015266 this_sequence A081300 A045640 A043040
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KEYWORD
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nonn
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AUTHOR
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Emeric Deutsch (deutsch(AT)duke.poly.edu), Mar 28 2008
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