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A269042 Number of permutations of [2n] avoiding the pattern 12...n. 4
0, 0, 1, 132, 15767, 2190688, 370531683, 77182248916, 19835792076675, 6266271456118776, 2413632612087046844, 1120958514818713738544, 619918692943471064695593, 403190647991638511052901232, 304867528413299672718870216538, 265248225675908889875489731636920 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..30

FORMULA

a(n) = (2n)! - A269021(n).

a(n) = A214015(2n,n-1) for n>0.

a(n) ~ (2*n)!. - Vaclav Kotesovec, Mar 26 2016

EXAMPLE

a(2) = 1: 4321.

a(3) = 132: 165432, 216543, 261543, 265143, 265413, 265431, 316542, ..., 653412, 653421, 654132, 654213, 654231, 654312, 654321.

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, 0, g(2*n, n-1, [])):

seq(a(n), n=0..15);

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, 0, g[2n, n-1, {}]];

Table[a[n], {n, 0, 15}] (* Jean-Fran├žois Alcover, Apr 01 2017, translated from Maple *)

CROSSREFS

Cf. A010050, A214015, A267532, A269021.

Sequence in context: A035818 A258394 A215546 * A216787 A239817 A175410

Adjacent sequences:  A269039 A269040 A269041 * A269043 A269044 A269045

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Feb 18 2016

STATUS

approved

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Last modified April 16 15:47 EDT 2021. Contains 343050 sequences. (Running on oeis4.)