A230341 Number of permutations of [2n] in which the longest increasing run has length n.

1, 1, 16, 293, 5811, 133669, 3574957, 109546009, 3788091451, 145957544981, 6201593613645, 288084015576169, 14525808779580645, 790129980885855401, 46120599397152203401, 2875600728737862162481, 190740227037467026439611, 13411608375592255857753781

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..300

Formula

a(n) = A008304(2*n,n).

Recurrence (of order 3): n*(n+2)*(12*n^7 - 101*n^6 + 355*n^5 - 668*n^4 + 631*n^3 - 71*n^2 - 344*n + 174)*a(n) = (n+1)*(48*n^9 - 272*n^8 + 453*n^7 - 10*n^6 - 518*n^5 - 741*n^4 + 4090*n^3 - 5810*n^2 + 3444*n - 720)*a(n-1) - 2*n*(2*n - 3)*(60*n^8 - 277*n^7 + 365*n^6 - 59*n^5 - 549*n^4 + 1619*n^3 - 2101*n^2 + 1228*n - 268)*a(n-2) + 4*(n-1)*(2*n - 5)*(2*n - 3)*(12*n^7 - 17*n^6 + n^5 + 12*n^4 - 91*n^3 + 101*n^2 - 12*n - 12)*a(n-3). - Vaclav Kotesovec, Jul 16 2014

a(n) ~ 2^(2*n+1/2)* n^(n+1) / exp(n). - Vaclav Kotesovec, Jul 16 2014

Maple

a:= proc(n) option remember; `if`(n<5, [1, 1, 16, 293, 5811][n+1],
      (2*(n+1)*(26615475780292426*n^4 +2862121494132556*n^3
        -240402559504315639*n^2 +79488454158677567*n
        +119546195807549142)*a(n-1)
      -n*(406022528821033256*n^4 -1031369150352151615*n^3
        +11028208356875758*n^2 -1654923205028490137*n
        +3900125789057762682)*a(n-2)
      +2*(n-1)*(421508861354067594*n^4 -1543365451253363033*n^3
        -602924004257000736*n^2 +6654606478117189961*n
        -5221800341103267066)*a(n-3)
      -4*(2*n-7)*(n-2)*(26655798868586248*n^3 +401269836638339496*n^2
        -2000296275137853913*n +2124466470996744981)*a(n-4)
      -8*(n-3)*(n-5)*(2*n-7)*(2*n-9)*(8655617328093650*n
        -14323734034655567)*a(n-5)) / (n*(n+2)*(13307737890146213*n^2
        -43906954139467620*n +22672341406878775)))
    end:
seq(a(n), n=0..25);

Mathematica

b[u_, o_, t_, k_] := b[u, o, t, k] = If[t == k, (u + o)!, If[Max[t, u] + o < k, 0, Sum[b[u + j - 1, o - j, t + 1, k], {j, 1, o}] + Sum[b[u - j, o + j - 1, 1, k], {j, 1, u}]]];
T[n_, k_] := b[0, n, 0, k] - b[0, n, 0, k + 1];
a[n_] := T[2n, n];
Table[a[n], {n, 0, 20}] (* Jean-François Alcover, Jul 19 2018, after Alois P. Heinz *)

Crossrefs

A diagonal of A008304.

Cf. A267433.

Sequence in context: A202878 A372172 A183886 * A278304 A298192 A299086

Adjacent sequences: A230338 A230339 A230340 * A230342 A230343 A230344

Keyword

nonn

Author

Alois P. Heinz, Oct 16 2013

Status

approved