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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

Alois P. Heinz, Table of n, a(n) for n = 3..110

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

Column k=3 of A262372.

Sequence in context: A153568 A153531 A153560 * A331957 A134956 A011803

Adjacent sequences:  A321056 A321057 A321058 * A321060 A321061 A321062

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Oct 26 2018

STATUS

approved

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Last modified January 19 06:18 EST 2022. Contains 350464 sequences. (Running on oeis4.)