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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..55

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: A158817 A159707 A097818 * A175411 A027725 A265239

Adjacent sequences:  A262376 A262377 A262378 * A262380 A262381 A262382

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Sep 20 2015

STATUS

approved

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Last modified July 2 18:27 EDT 2022. Contains 355029 sequences. (Running on oeis4.)