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A262233 Number of ordered pairs (p,q) of permutations of [n] with equal up-down signatures and p(1)=1 if n>0. 4
1, 1, 1, 3, 20, 220, 3648, 84616, 2617696, 104112576, 5176135040, 314525766016, 22934467613184, 1976385358538240, 198701625441195520, 23050434113386398720, 3055967615464202301440, 459172688072604359835648, 77616824553405653653094400 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..110

EXAMPLE

a(1) = 1: (1,1).

a(2) = 1: (12,12).

a(3) = 3: (123,123), (132,132), (132,231).

a(4) = 20: (1234,1234), (1243,1243), (1243,1342), (1243,2341), (1324,1324), (1324,1423), (1324,2314), (1324,2413), (1324,3412), (1342,1243), (1342,1342), (1342,2341), (1423,1324), (1423,1423), (1423,2314), (1423,2413), (1423,3412), (1432,1432), (1432,2431), (1432,3421).

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-> `if`(n=0, 1, add(b(j-1, n-j, n-1), j=1..n)):

seq(a(n), n=0..20);

CROSSREFS

Cf. A060350, A262234, A262241.

Sequence in context: A113333 A206405 A052851 * A058477 A119758 A108527

Adjacent sequences:  A262230 A262231 A262232 * A262234 A262235 A262236

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Sep 15 2015

STATUS

approved

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Last modified February 20 12:33 EST 2018. Contains 299379 sequences. (Running on oeis4.)