A230133 Number of permutations of order n with the length of longest run equal 10.

2, 40, 698, 11908, 206388, 3690960, 68577600, 1327697280, 26812356480, 564796979240, 12403183337690, 283718956204402, 6753363090218970, 167092903876164794, 4292602805804464576, 114374394103260000000, 3157276569203744863200, 90202107365906127228000

Offset: 10

Author

Alois P. Heinz, Oct 10 2013

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 10..450

Crossrefs

Column l=10 of A211318.

A diagonal of A010026.

Programs

Maple

g:= proc(u, o, t) option remember; `if`(u+o=0, 1,
       add(g(o+j-1, u-j, 2), j=1..u) +`if`(t<10,
       add(g(u+j-1, o-j, t+1), j=1..o), 0))
    end:
b:= proc(u, o, t) option remember; `if`(t=10, g(u, o, t),
       add(b(o+j-1, u-j, 2), j=1..u)+
       add(b(u+j-1, o-j, t+1), j=1..o))
    end:
a:= n-> add(b(j-1, n-j, 1), j=1..n):
seq(a(n), n=10..30);

Mathematica

length = 10;
g[u_, o_, t_] := g[u, o, t] = If[u+o == 0, 1, Sum[g[o + j - 1, u - j, 2], {j, 1, u}] + If[tJean-François Alcover, Aug 18 2018, after Alois P. Heinz *)