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A217324 Number of self-inverse permutations in S_n with longest increasing subsequence of length 4. 2
1, 4, 19, 69, 265, 929, 3356, 11626, 41117, 142206, 499836, 1734328, 6099193, 21282265, 75125770, 263906332, 936517637, 3313246237, 11827430209, 42139231729, 151339387003, 542857007499, 1961171657524, 7079621540798, 25720257983591, 93396276789196 (list; graph; refs; listen; history; text; internal format)
OFFSET

4,2

COMMENTS

Also the number of Young tableaux with n cells and 4 rows.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 4..1000

FORMULA

a(n) = A182172(n,4)-A182172(n,3) = A005817(n)-A001006(n).

EXAMPLE

a(4) = 1: 1234.

a(5) = 4: 12354, 12435, 13245, 21345.

a(6) = 19: 123654, 124365, 125436, 125634, 126453, 132465, 132546, 143256, 145236, 153426, 163452, 213465, 213546, 214356, 321456, 341256, 423156, 523416, 623451.

MAPLE

a:= proc(n) option remember; `if`(n<4, 0, `if`(n=4, 1,

      ((2+n)*(30*n^5+199*n^4-374*n^3-1537*n^2-406*n+408)*a(n-1)

       -4*(n-1)*(n-2)*(120*n^4+46*n^3-471*n^2+371*n+204)*a(n-3)

       +(n-1)*(285*n^5-262*n^4-2755*n^3-1520*n^2+820*n-48)*a(n-2)

       -48*(n-1)*(n-3)*(3*n+7)*(5*n+4)*(n-2)^2*a(n-4))/

      ((n-4)*(5*n-1)*(3*n+4)*(n+4)*(n+3)*(n+2))))

    end:

seq(a(n), n=4..40);

CROSSREFS

Column k=4 of A047884.

Cf. A001006, A005817, A182172.

Sequence in context: A055485 A000306 A100185 * A129019 A167247 A267192

Adjacent sequences:  A217321 A217322 A217323 * A217325 A217326 A217327

KEYWORD

nonn,easy

AUTHOR

Alois P. Heinz, Sep 30 2012

STATUS

approved

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Last modified March 25 00:04 EDT 2017. Contains 284035 sequences.