A217675 Number of permutations in S_n containing an increasing subsequence of length 8.

1, 65, 2603, 83923, 2410291, 64864819, 1683724308, 42918747000, 1086997811325, 27571922195325, 704311698875426, 18189847735254134, 476311846323448840, 12672229166094171240, 343069245941729668380, 9461927811882316662636, 266091066751920438364275

Offset: 8

Author

Alois P. Heinz, Oct 10 2012

Keywords

• nonn

Examples

			a(8) = 1: 12345678.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 8..200

Crossrefs

Cf. A000142, A072131, A214015, A214152.

Programs

Maple

b:= proc(n) option remember; `if`(n<8, n!, ((-343035+429858*n
       +238440*n^3+38958*n^4+634756*n^2+2940*n^5+84*n^6)*b(n-1)
       -(1974*n^4+36336*n^3+213240*n^2+407840*n+82425)*(n-1)^2*b(n-2)
       +2*(49875+42646*n+6458*n^2)*(n-1)^2*(n-2)^2*b(n-3)
       -11025*(n-1)^2*(n-2)^2*(n-3)^2*b(n-4))/ ((n+6)^2*(n+10)^2*(n+12)^2))
    end:
a:= n-> n! -b(n):
seq(a(n), n=8..25);

Formula

a(n) = A214152(n,8) = A000142(n)-A072131(n) = A000142(n)-A214015(n,7).