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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: A159707 A097818 A360195 * 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 September 18 06:21 EDT 2024. Contains 375996 sequences. (Running on oeis4.)