A028304 a(n) = ceiling( binomial(n, floor(n/2))/(1 + ceiling(n/2)) ) (interpolates between Catalan numbers).

1, 1, 1, 1, 2, 3, 5, 7, 14, 21, 42, 66, 132, 215, 429, 715, 1430, 2431, 4862, 8398, 16796, 29393, 58786, 104006, 208012, 371450, 742900, 1337220, 2674440, 4847423, 9694845, 17678835, 35357670, 64822395, 129644790, 238819350, 477638700, 883631595, 1767263190, 3282060210

Offset

0,5

References

D. Miklós, Vera T. Sós, and T. Szőnyi, eds., Combinatorics, Paul Erdős is Eighty, Bolyai Math. Soc., 1993, Vol. 1, p. 101.

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Formula

a(2*n) = A000108(n), a(2*n+1) = A130380(n+1). - R. J. Mathar, Dec 15 2015

a(n) = ceiling(A001405(n)/A004526(n+3)). - G. C. Greubel, Jan 05 2024

a(n) ~ 2^(n+3/2) / (n^(3/2) * sqrt(Pi)). - Amiram Eldar, Sep 25 2025

Maple

A028304 := proc(n)
    A001405(n)/(ceil(n/2)+1) ;
    ceil(%) ;
end proc: # R. J. Mathar, Dec 15 2015

Mathematica

Table[Ceiling[(1/(Ceiling[n/2] + 1)) Binomial[n, Floor[n/2]]], {n, 0, 49}] (* Alonso del Arte, Oct 30 2019 *)

Prog

(Magma) [Ceiling(Binomial(n, Floor(n/2))/Floor((n+3)/2)): n in [0..50]]; // G. C. Greubel, Jan 05 2024
(SageMath) [ceil(binomial(n, int(n/2))/((n+3)//2)) for n in range(51)] # G. C. Greubel, Jan 05 2024

Crossrefs

Cf. A000108, A000245, A001405, A004526, A130380.

Sequence in context: A046808 A097799 A005629 * A324840 A316475 A303875

Adjacent sequences: A028301 A028302 A028303 * A028305 A028306 A028307

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved