A217325 Number of self-inverse permutations in S_n with longest increasing subsequence of length 5.

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

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: A267921 A241676 A291889 * A034332 A273027 A268957

Adjacent sequences: A217322 A217323 A217324 * A217326 A217327 A217328

Keyword

nonn

Author

Alois P. Heinz, Sep 30 2012

Status

approved