|
|
A321059
|
|
Number of ordered pairs (p,q) of permutations of [n] with equal up-down signatures and p(1)=q(1)=3.
|
|
2
|
|
|
2, 8, 64, 852, 17008, 467696, 16860608, 769534688, 43316046592, 2945846638464, 238048843712512, 22542120635302912, 2472277850712350720, 310880199760083564032, 44429722692959679590400, 7161345941202962487965696, 1292988538929694918729072640
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
3,1
|
|
LINKS
|
|
|
EXAMPLE
|
a(3) = 2: (312,312), (321,321).
a(4) = 8: (3124,3124), (3142,3142), (3142,3241), (3214,3214), (3241,3142), (3241,3241), (3412,3412), (3421,3421).
|
|
MAPLE
|
b:= proc(u, o, h) option remember; `if`(u+o=0, 1,
add(add(b(u-j, o+j-1, h+i-1), i=1..u+o-h), j=1..u)+
add(add(b(u+j-1, o-j, h-i), i=1..h), j=1..o))
end:
a:= n-> (k-> b(k-1, n-k, n-k))(3):
seq(a(n), n=3..20);
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|