A267436 Number of self-inverse permutations of [2n] with longest increasing subsequence of length n.

1, 1, 5, 31, 265, 2446, 26069, 294386, 3628517, 46938514, 645978814, 9265791393, 139408562319, 2174338555026, 35259402634616, 590187761512336, 10209739522685893, 181678453872654154, 3326776921054665350, 62485419303819431072, 1203772979032614462448

Offset: 0

Author

Alois P. Heinz, Jan 15 2016

Keywords

• nonn

Comments

Also the number of 2n-length words w over n-ary alphabet {a1,a2,...,an} such that for every prefix z of w we have #(z,a1) >= #(z,a2) >= ... >= #(z,an) >= 1, where #(z,x) counts the letters x in word z. The a(2) = 5 words of length 4 over alphabet {a,b} are: aaab, aaba, abaa, aabb, abab.

Examples

			a(2) = 5: 1432, 2143, 3214, 3412, 4231.
		

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..70 (terms 0..55 from Alois P. Heinz)

Crossrefs

Cf. A047884, A267433, A293128.

Programs

Maple

h:= proc(l) local n; n:= nops(l); 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) end:
g:= (n, i, l)-> `if`(n=0 or i=1, h([l[], 1$n]), add(
                g(n-i*j, i-1, [l[], i$j]), j=0..n/i)):
a:= n-> g(n$2, [n]):
seq(a(n), n=0..25);

Mathematica

h[l_] := With[{n = Length[l]}, 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}]];
g[n_, i_, l_] := If[n == 0 || i == 1, h[Join[l, Table[1, {n}]]], Sum[g[n - i*j, i - 1, Join[l, Table[i, {j}]]], {j, 0, n/i}]];
a[n_] := g[n, n, {n}];
a /@ Range[0, 25] (* Jean-François Alcover, Jan 02 2021, after Alois P. Heinz *)

Formula

a(n) = A047884(2n,n).