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A269021 Number of permutations of [2n] containing an increasing subsequence of length n. 3
1, 2, 23, 588, 24553, 1438112, 108469917, 9996042284, 1086997811325, 136102249609224, 19269396089593156, 3042212958893941456, 529708789768374664407, 100813134967124531098768, 20816198414187782633783462, 4634136282168760818748363080 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Alois P. Heinz and Vaclav Kotesovec, Table of n, a(n) for n = 0..41 (terms 0..30 from Alois P. Heinz)

FORMULA

a(n) = A214152(2n,n).

a(n) = (2n)! - A269042(n).

a(n) ~ 16^n * (n-1)! / (Pi * exp(2)). - Vaclav Kotesovec, Mar 27 2016

EXAMPLE

a(1) = 2: 12, 21.

a(2) = 23: all 4! permutations of {1,2,3,4} with the exception of 4321.

MAPLE

h:= proc(l) (n-> add(i, i=l)!/mul(mul(1+l[i]-j+add(`if`(

      l[k]>=j, 1, 0), k=i+1..n), j=1..l[i]), i=1..n))(nops(l))

    end:

g:= (n, i, l)-> `if`(n=0 or i=1, h([l[], 1$n])^2, `if`(i<1, 0,

                 add(g(n-i*j, i-1, [l[], i$j]), j=0..n/i))):

a:= n-> `if`(n=0, 1, (2*n)!-g(2*n, n-1, [])):

seq(a(n), n=0..16);

MATHEMATICA

h[l_] := Function[n, Total[l]!/Product[Product[1+l[[i]]-j+Sum[If[l[[k]] >= j, 1, 0], {k, i+1, n}], {j, 1, l[[i]]}], {i, 1, n}]][Length[l]];

g[n_, i_, l_] := If[n == 0 || i == 1, h[Join[l, Table[1, {n}]]]^2, If[i < 1, 0, Sum[g[n - i*j, i - 1, Join[l, Table[i, {j}]]], {j, 0, n/i}]]];

a[n_] := If[n == 0, 1, (2n)! - g[2n, n-1, {}]];

Table[a[n], {n, 0, 16}] (* Jean-Fran├žois Alcover, Apr 01 2017, translated from Maple *)

CROSSREFS

Cf. A010050, A214152, A269042.

Sequence in context: A084322 A073062 A015098 * A136039 A237580 A273976

Adjacent sequences:  A269018 A269019 A269020 * A269022 A269023 A269024

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Feb 17 2016

STATUS

approved

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Last modified May 16 12:30 EDT 2021. Contains 343947 sequences. (Running on oeis4.)