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A262379
Number of ordered pairs (p,q) of permutations of [2n] with equal up-down signatures and p(1)=q(1)=n.
2
1, 1, 8, 852, 438496, 678914816, 2475764410944, 18237517555977472, 244043425473888612352, 5486719044572824902107136, 195206678980725195413273903104, 10481263341014180286866656598294528, 817228517264548077840269973629276061696
OFFSET
0,3
LINKS
FORMULA
a(n) = A262372(2n,n).
EXAMPLE
a(2) = 8: (2134,2134), (2143,2143), (2314,2314), (2314,2413), (2341,2341), (2413,2314), (2413,2413), (2431,2431).
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-> `if`(n=0, 1, b(n-1, n, n)):
seq(a(n), n=0..15);
CROSSREFS
Cf. A262372.
Sequence in context: A159707 A097818 A360195 * A175411 A027725 A265239
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Sep 20 2015
STATUS
approved