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A371698
Number of partial order-preserving or -reversing transformations of a chain of length n.
0
2, 9, 54, 323, 1848, 10293, 56738, 312327, 1723692, 9549785, 53121654, 296593547, 1661423104, 9333552509, 52565738570, 296696569871, 1677887732820, 9505147063713, 53928737011358, 306393222740883, 1742919983985192, 9925790283119429, 56584658970159474, 322879453747840023
OFFSET
1,1
LINKS
V. H. Fernandes, G. M. S. Gomes, and M. M. Jesus, Presentations for some monoids of partial transformations on a finite chain, Communications in Algebra, 33 (2005), 587-604, 2005.
FORMULA
a(n) = 4*Sum_{k=0..n-1} binomial(n-1, k)*binomial(n+k, k) - (1 + n*(2 ^ n - 1)).
a(n) = 2*A002003(n) - (1 + n*(2^n - 1)).
PROG
(GAP) n -> 4 * Sum([0 .. n - 1], k -> Binomial(n - 1, k) * Binomial(n + k, k)) - (1 + n * (2 ^ n - 1));
(PARI) a(n) = 4 * sum(k=0, n-1, binomial(n -1, k)*binomial(n + k, k)) - (1 + n * (2 ^ n - 1)); \\ Michel Marcus, Apr 03 2024
CROSSREFS
Cf. A002003.
Sequence in context: A360454 A073986 A223943 * A241125 A370474 A089436
KEYWORD
nonn
AUTHOR
James Mitchell, Apr 03 2024
STATUS
approved