A028303 a(n) = floor( binomial(n, floor(n/2))/(1 + ceiling(n/2)) ) (interpolates between Catalan numbers).

1, 0, 1, 1, 2, 2, 5, 7, 14, 21, 42, 66, 132, 214, 429, 715, 1430, 2431, 4862, 8398, 16796, 29393, 58786, 104006, 208012, 371450, 742900, 1337220, 2674440, 4847422, 9694845, 17678835, 35357670, 64822395, 129644790, 238819350, 477638700, 883631595, 1767263190

Offset

0,5

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

Formula

a(n) = floor(A001405(n)/A004526(n+3)). - G. C. Greubel, Jan 04 2024

Mathematica

Table[Floor[Binomial[n, Floor[n/2]]/Floor[(n+3)/2]], {n, 0, 50}] (* G. C. Greubel, Jan 04 2024 *)

Prog

(Magma) [Floor(Binomial(n, Floor(n/2))/Floor((n+3)/2)): n in [0..50]]; // G. C. Greubel, Jan 04 2024
(SageMath) [int(binomial(n, int(n/2))/((n+3)//2)) for n in range(51)] # G. C. Greubel, Jan 04 2024

Crossrefs

Cf. A000108, A001405, A004526.

Sequence in context: A036378 A265813 A259864 * A255063 A195964 A238422

Adjacent sequences: A028300 A028301 A028302 * A028304 A028305 A028306

Keyword

nonn

Author

N. J. A. Sloane

Status

approved