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A344898 Number of equivalence classes of pairs of permutations on S2n where 2 pairs are equivalent if they generate similar maps on Dyck paths. 0
1, 3, 154, 8369, 711226, 90349957, 16012077362, 3768789527617, 1136241039871954, 426747190631335301, 195301450278484563322, 106968871128338892427537, 69076413764424335543681642, 51931946172675368683512111589, 44964793280161619728525791864226, 44419470206051792513510236597094657 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,2

COMMENTS

Needs another program to check formula and current program. See discussions.

LINKS

Table of n, a(n) for n=2..17.

Kevin Limanta, Hopein Christofen Tang, and Yozef Tjandra, Permutation-generated maps between Dyck paths, arXiv:2105.14439 [math.CO], 2021.

FORMULA

a(n) = 1 - n^2 + 2*Sum_{a=1, n-1} Sum_{b=1, n-1} n!^2*(binomial(2*n-2-a-b, n-2)+binomial(2*n-2-a-b, n-1-a))/(max(a,2)!*max(b,2)!).

PROG

(PARI) a(n) = 1 - n^2 + 2*sum(a=1, n-1, sum(b=1, n-1, n!^2*(binomial(2*n-2-a-b, n-2)+binomial(2*n-2-a-b, n-1-a))/(max(a, 2)!*max(b, 2)!)));

CROSSREFS

Sequence in context: A039934 A156990 A075514 * A327058 A087306 A278877

Adjacent sequences:  A344895 A344896 A344897 * A344899 A344900 A344901

KEYWORD

nonn

AUTHOR

Michel Marcus, Jun 01 2021

STATUS

approved

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Last modified January 24 12:11 EST 2022. Contains 350536 sequences. (Running on oeis4.)