A079103 - OEIS

A079103

a(n) = Catalan(n)^(2*n-2).

1, 1, 4, 625, 7529536, 9682651996416, 1605976966052654874624, 38858631894268190306056236008241, 149521802722388792654037601564900000000000000, 97507780747332761768395977098452480878573838263199129993216, 11316329577423677140600642130598798092495455542306819767463118769921915355136

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OFFSET

0,3

COMMENTS

For n >= 3, the number of permutations of length n*(2*n-1) in which all monotone subsequences of length n+1 are descending and the number of them is minimal.

LINKS

Table of n, a(n) for n=0..10.

Joseph Myers, The minimum number of monotone subsequences, Electronic J. Combin. 9(2) (2002), #R4.

Joseph Myers, The list for n=3

MAPLE

a:= n-> (binomial(2*n, n)/(n+1))^(2*n-2):

seq(a(n), n=0..10); # Alois P. Heinz, Nov 08 2025

MATHEMATICA

Table[CatalanNumber[n]^(2n-2), {n, 10}] (* Harvey P. Dale, Oct 24 2011 *)

CROSSREFS

Cf. A000108, A001246, A079102, A079104, A079105, A079106.

Sequence in context: A210853 A232620 A219892 * A191953 A169619 A337650