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%I #9 Jul 28 2023 21:04:37
%S 1,1,2,4,12,36,116,382,1287,4420,15397,54264,193154,693374,2507288,
%T 9124560,33393355,122821380,453756765,1683107800,6265751310,
%U 23402516280,87670790155,329337229104,1240292449350,4681874312510,17711376176718,67135842263728,254956353358682
%N A Catalan-like sequence.
%C 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?
%D Felix Goldberg, A problem relating to a family of Catalan-like sequences, forthcoming.
%F 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).
%e a(6) = 116 because 1/(6+2)*C(12,6) is 115.5 and taking the ceiling we obtain 116.
%p a:= n-> ceil(binomial(2*n, n)/(n+2)):
%p seq(a(n), n=0..28); # _Alois P. Heinz_, Jul 28 2023
%Y Cf. A000108.
%K nonn
%O 0,3
%A Felix Goldberg (sgefelix(AT)t2.technion.ac.il), Apr 10 2000
%E More terms from _James A. Sellers_, Apr 11 2000
%E a(0)=1 prepended by _Alois P. Heinz_, Jul 28 2023