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A054542
A Catalan-like sequence.
1
1, 1, 2, 4, 12, 36, 116, 382, 1287, 4420, 15397, 54264, 193154, 693374, 2507288, 9124560, 33393355, 122821380, 453756765, 1683107800, 6265751310, 23402516280, 87670790155, 329337229104, 1240292449350, 4681874312510, 17711376176718, 67135842263728, 254956353358682
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
Cf. A000108.
Sequence in context: A217699 A291190 A273955 * A214198 A117757 A009623
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