A217676 Number of permutations in S_n containing an increasing subsequence of length 9.

1, 82, 4062, 159404, 5497718, 175652924, 5360393100, 159281625000, 4667810722500, 136102249609224, 3973117419487320, 116645785269445696, 3455520662446396976, 103544836992023092832, 3144187412886704149472, 96883566754646092037696, 3032518386648514382974097

Offset

9,2

Links

Alois P. Heinz, Table of n, a(n) for n = 9..200

Formula

a(n) = A214152(n,9) = A000142(n)-A072132(n) = A000142(n)-A214015(n,8).

Example

a(9) = 1: 123456789.

Maple

b:= proc(n) option remember; `if`(n<4, n!,
      (-147456*(n+4)*(n-1)^2*(n-2)^2*(n-3)^2*b(n-4)
      +128*(33876+30709*n+6687*n^2+410*n^3)*(n-1)^2*(n-2)^2*b(n-3)
      -4*(1092*n^5+37140*n^4+455667*n^3+2387171*n^2+4649270*n+1206000)*
      (n-1)^2*b(n-2) +(-17075520+(22488312+(29223280+(10509820+(1764252+
      (154164+(6804+120*n)*n)*n)*n)*n)*n)*n)*b(n-1))/
      ((n+16)*(n+7)^2*(n+15)^2*(n+12)^2))
    end:
a:= n-> n! -b(n):
seq(a(n), n=9..30);

Crossrefs

Cf. A000142, A072132, A214015, A214152.

Sequence in context: A017798 A035736 A017745 * A203169 A214815 A280959

Adjacent sequences: A217673 A217674 A217675 * A217677 A217678 A217679

Keyword

nonn

Author

Alois P. Heinz, Oct 10 2012

Status

approved