A054542 A Catalan-like sequence.

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.

Links

Table of n, a(n) for n=0..28.

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

Adjacent sequences: A054539 A054540 A054541 * A054543 A054544 A054545

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