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A217676 Number of permutations in S_n containing an increasing subsequence of length 9. 3
1, 82, 4062, 159404, 5497718, 175652924, 5360393100, 159281625000, 4667810722500, 136102249609224, 3973117419487320, 116645785269445696, 3455520662446396976, 103544836992023092832, 3144187412886704149472, 96883566754646092037696, 3032518386648514382974097 (list; graph; refs; listen; history; text; internal format)
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

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Last modified September 23 02:41 EDT 2021. Contains 347609 sequences. (Running on oeis4.)