cp's OEIS Frontend

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

%I A230133 #12 Aug 18 2018 08:38:21
%S A230133 2,40,698,11908,206388,3690960,68577600,1327697280,26812356480,
%T A230133 564796979240,12403183337690,283718956204402,6753363090218970,
%U A230133 167092903876164794,4292602805804464576,114374394103260000000,3157276569203744863200,90202107365906127228000
%N A230133 Number of permutations of order n with the length of longest run equal 10.
%H A230133 Alois P. Heinz, <a href="/A230133/b230133.txt">Table of n, a(n) for n = 10..450</a>
%p A230133 g:= proc(u, o, t) option remember; `if`(u+o=0, 1,
%p A230133        add(g(o+j-1, u-j, 2), j=1..u) +`if`(t<10,
%p A230133        add(g(u+j-1, o-j, t+1), j=1..o), 0))
%p A230133     end:
%p A230133 b:= proc(u, o, t) option remember; `if`(t=10, g(u, o, t),
%p A230133        add(b(o+j-1, u-j, 2), j=1..u)+
%p A230133        add(b(u+j-1, o-j, t+1), j=1..o))
%p A230133     end:
%p A230133 a:= n-> add(b(j-1, n-j, 1), j=1..n):
%p A230133 seq(a(n), n=10..30);
%t A230133 length = 10;
%t A230133 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[t<length, Sum[g[u + j - 1, o - j, t+1], {j, 1, o}], 0]];
%t A230133 b[u_, o_, t_] := b[u, o, t] = If[t == length, g[u, o, t], Sum[b[o + j - 1, u - j, 2], {j, 1, u}] + Sum[b[u + j - 1, o - j, t + 1], {j, 1, o}]];
%t A230133 a[n_] := Sum[b[j - 1, n - j, 1], {j, 1, n}];
%t A230133 Table[a[n], {n, length, 30}] (* _Jean-François Alcover_, Aug 18 2018, after _Alois P. Heinz_ *)
%Y A230133 Column l=10 of A211318.
%Y A230133 A diagonal of A010026.
%K A230133 nonn
%O A230133 10,1
%A A230133 _Alois P. Heinz_, Oct 10 2013