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
KEYWORD
nonn
AUTHOR
James Mitchell, Apr 03 2024
STATUS
approved