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

Author

Alois P. Heinz, Sep 30 2012

Keywords

• nonn

Comments

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

Examples

			a(5) = 1: 12345.
a(6) = 5: 123465, 123546, 124356, 132456, 213456.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 5..1449 (terms 501..1000 from Seiichi Manyama)

Crossrefs

Column k=5 of A047884.

Cf. A005817, A049401, A182172.

Programs

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
       [phone]*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
       [phone]*n [phone])*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);

Formula

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