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A217325 Number of self-inverse permutations in S_n with longest increasing subsequence of length 5. 2
1, 5, 29, 127, 583, 2446, 10484, 43363, 181546, 748840, 3114308, 12878441, 53594473, 222761422, 930856456, 3893811380, 16365678160, 68937445765, 291656714515, 1237403762663, 5271285939671, 22524961082326, 96620152734652, 415768621923904, 1795530067804295 (list; graph; refs; listen; history; text; internal format)
OFFSET

5,2

COMMENTS

Also the number of Young tableaux with n cells and 5 rows.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 5..500

FORMULA

a(n) = A182172(n,5)-A182172(n,4) = A049401(n)-A005817(n).

EXAMPLE

a(5) = 1: 12345.

a(6) = 5: 123465, 123546, 124356, 132456, 213456.

MAPLE

a:= proc(n) option remember; `if`(n<5, 0, `if`(n=5, 1,

     ((n+3)*(166075637*n^5+3319452867*n^4+10706068615*n^3-39910302747*n^2

       -182846631872*n-159926209260)*a(n-1) +(840221898216*n+133982123900

       -322021480097*n^3-83890810854*n^4+12016871251*n^5+3735622433*n^6

       +111397917411*n^2)*a(n-2)-(n-2)*(2142183361*n^5+66617759078*n^4

       -47640468971*n^3-611402096064*n^2+15449945364*n+452645243780)*a(n-3)

       -(n-2)*(n-3)*(33769818805*n^4-54918997862*n^3 -469629276839*n^2

       +789889969148*n +94438295920)*a(-4+n) -4*(n-2)*(n-3)*(-4+n)*

       (2060107324*n^3 -87569131518*n^2+293565842963*n -151080184425)*a(n-5)

       +240*(n-2)*(n-3)*(n-5)*(168175627*n-312397451)*(-4+n)^2*a(n-6))/

       (8*(13927136*n+37088781)*(n-5)*(n+6)*(n+4)*(n+3)^2)))

    end:

seq (a(n), n=5..40);

CROSSREFS

Column k=5 of A047884.

Cf. A005817, A049401, A182172.

Sequence in context: A000352 A267921 A241676 * A034332 A273027 A268957

Adjacent sequences:  A217322 A217323 A217324 * A217326 A217327 A217328

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Sep 30 2012

STATUS

approved

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Last modified July 24 18:02 EDT 2017. Contains 289776 sequences.