A217677 Number of permutations in S_n containing an increasing subsequence of length 10.

1, 101, 6063, 284431, 11592572, 433386000, 15343169775, 524963196399, 17597634740010, 583499409451862, 19269396089593156, 636977450902768356, 21156201514272916444, 708006643310351350076, 23925259865186482138965, 817728884509460388159381

Offset: 10

Author

Alois P. Heinz, Oct 10 2012

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 10..200

Crossrefs

Cf. A000142, A072133, A214015, A214152.

Programs

Maple

b:= proc(n) option remember;
      `if`(n<5, n!, ((-1110790863+(1520978576+(1772290401+(607308786+
       (101671498+(9464664+(500874+(14124+165*n)*n)*n)*n)*n)*n)*n)*n)*b(n-1)
       -(1129886062*n+559908333*n^2+111239576*n^3+10655238*n^4+8778*n^6
       +491700*n^5 [phone])*(n-1)^2*b(n-2) +(258011271+234066216*n
       [phone]*n^2+5463876*n^3 +172810*n^4)*(n-1)^2*(n-2)^2*b(n-3)
       -9*(4070430+1504292*n+117469*n^2)* (n-1)^2*(n-2)^2*(n-3)^2*b(n-4)
       +893025*(n-1)^2*(n-2)^2*(n-3)^2*(n-4)^2*b(n-5)) /
       ((n+20)^2*(n+8)^2*(n+18)^2*(n+14)^2))
    end:
a:= n-> n! -b(n):
seq(a(n), n=10..30);

Formula

a(n) = A214152(n,10) = A000142(n)-A072133(n) = A000142(n)-A214015(n,9).