OFFSET
0,3
COMMENTS
This sequence (k=2, p=2) belongs to a family of Catalan-like sequences that merit further investigation. The ceiling is taken in order to eliminate the fractional parts. Are there combinations of k and p for which the ceiling is unnecessary?
REFERENCES
Felix Goldberg, A problem relating to a family of Catalan-like sequences, forthcoming.
FORMULA
a(n) = ceiling( 1/(n+k)*C(p*n,n) ), where k=2, p=2 (in the standard Catalan sequence k=1 and p=2).
EXAMPLE
a(6) = 116 because 1/(6+2)*C(12,6) is 115.5 and taking the ceiling we obtain 116.
MAPLE
a:= n-> ceil(binomial(2*n, n)/(n+2)):
seq(a(n), n=0..28); # Alois P. Heinz, Jul 28 2023
CROSSREFS
KEYWORD
nonn
AUTHOR
Felix Goldberg (sgefelix(AT)t2.technion.ac.il), Apr 10 2000
EXTENSIONS
More terms from James A. Sellers, Apr 11 2000
a(0)=1 prepended by Alois P. Heinz, Jul 28 2023
STATUS
approved