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A317448 Number of permutations of [n] whose lengths of increasing runs are distinct factorial numbers. 6

%I

%S 1,1,1,4,0,0,1,12,54,1002,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,48,648,39444,

%T 0,0,1187548,96978608,1721374454,169149221140,0,0,0,0,0,0,0,0,0,0,0,0,

%U 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0

%N Number of permutations of [n] whose lengths of increasing runs are distinct factorial numbers.

%H Alois P. Heinz, <a href="/A317448/b317448.txt">Table of n, a(n) for n = 0..721</a>

%F a(n) = 0 <=> n in { A115945 }.

%F a(n) > 0 <=> n in { A059590 }.

%p h:= proc(n) local i; 1; for i from 2 do

%p if n=% then 1; break elif n<% then 0; break fi;

%p %*i od; h(n):=%

%p end:

%p g:= (n, s)-> `if`(n in s or not (n=0 or h(n)=1), 0, 1):

%p b:= proc(u, o, t, s) option remember; `if`(u+o=0, g(t, s),

%p `if`(g(t, s)=1, add(b(u-j, o+j-1, 1, s union {t})

%p , j=1..u), 0)+ add(b(u+j-1, o-j, t+1, s), j=1..o))

%p end:

%p a:= n-> b(n, 0$2, {}):

%p seq(a(n), n=0..34);

%Y Cf. A000142, A059590, A115945, A317132, A317444, A317445, A317446, A317447.

%K nonn

%O 0,4

%A _Alois P. Heinz_, Jul 28 2018

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Last modified September 30 18:12 EDT 2020. Contains 337440 sequences. (Running on oeis4.)