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

10,2

Links

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

Formula

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

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 +353895381)*(n-1)^2*b(n-2) +(258011271+234066216*n
       +58221266*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);

Crossrefs

Cf. A000142, A072133, A214015, A214152.

Sequence in context: A166218 A167626 A017764 * A333689 A291990 A303572

Adjacent sequences: A217674 A217675 A217676 * A217678 A217679 A217680

Keyword

nonn

Author

Alois P. Heinz, Oct 10 2012

Status

approved