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URL: https://oeis.org/A217193

⇱ A217193 - OEIS

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A217193
Number of permutations in S_{n+3} containing an increasing subsequence of length n.
3
6, 24, 119, 588, 2279, 6996, 18043, 40884, 83923, 159404, 284431, 482108, 782799, 1225508, 1859379, 2745316, 3957723, 5586364, 7738343, 10540204, 14140151, 18710388, 24449579, 31585428, 40377379, 51119436, 64143103, 79820444, 98567263, 120846404, 147171171
OFFSET
0,1
LINKS
FORMULA
a(0) = 6, a(1) = 24, a(n) = (n^6+6*n^5+10*n^4+4*n^3+19*n^2+62*n+66)/6 for n>1.
G.f.: (4*x^8-23*x^7+53*x^6-60*x^5+32*x^4+49*x^3+77*x^2-18*x+6)/(1-x)^7.
EXAMPLE
a(2) = 119: only one of 5! = 120 permutations of {1,2,3,4,5} has no increasing subsequence of length 2: 54321.
MAPLE
a:= n-> 11+(62+(19+(4+(10+(6+n)*n)*n)*n)*n)*n/6-`if`(n<2, 5-n, 0):
seq(a(n), n=0..40);
MATHEMATICA
CoefficientList[Series[(4x^8-23x^7+53x^6-60x^5+32x^4+49x^3+77x^2-18x+6)/ (1-x)^7, {x, 0, 40}], x] (* or *) LinearRecurrence[{7, -21, 35, -35, 21, -7, 1}, {6, 24, 119, 588, 2279, 6996, 18043, 40884, 83923}, 50] (* Harvey P. Dale, Jul 28 2021 *)
CROSSREFS
A diagonal of A214152.
Sequence in context: A293257 A223752 A293236 * A109583 A377502 A352807
KEYWORD
nonn,easy
AUTHOR
Alois P. Heinz, Sep 27 2012
STATUS
approved