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

Author

Alois P. Heinz, Oct 10 2012

Keywords

• nonn

Examples

			a(9) = 1: 123456789.
		

Links

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

Crossrefs

Cf. A000142, A072132, A214015, A214152.

Programs

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);

Formula

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