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A317448 Number of permutations of [n] whose lengths of increasing runs are distinct factorial numbers. 6
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, 0, 0, 1187548, 96978608, 1721374454, 169149221140, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..721

FORMULA

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

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

MAPLE

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

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

      %*i od; h(n):=%

    end:

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

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

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

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

    end:

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

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

CROSSREFS

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

Sequence in context: A134832 A123163 A194794 * A292900 A177893 A058305

Adjacent sequences:  A317445 A317446 A317447 * A317449 A317450 A317451

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Jul 28 2018

STATUS

approved

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Last modified August 11 03:22 EDT 2020. Contains 336421 sequences. (Running on oeis4.)