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

Author

N. J. A. Sloane

Keywords

• nonn

References

• D. Miklos et al., 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

Crossrefs

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

Programs

Magma

[Ceiling(Binomial(n,Floor(n/2))/Floor((n+3)/2)): n in [0..50]]; // G. C. Greubel, Jan 05 2024

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 *)

SageMath

[ceil(binomial(n,int(n/2))/((n+3)//2)) for n in range(51)] # G. C. Greubel, Jan 05 2024

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