A188669 a(n) = ceiling(binomial(2*n-1,n-1)/n).

1, 2, 4, 9, 26, 77, 246, 805, 2702, 9238, 32066, 112674, 400024, 1432736, 5170584, 18783763, 68635478, 252087092, 930138522, 3446163221, 12815663678, 47820430994, 178987624514, 671825076732, 2528212128756, 9536894864387, 36054433808299, 136583760727865, 518401146543812, 1971076359414358, 7506908923471954, 28634752202227978

Offset: 1

Author

Robert Gerbicz and N. J. A. Sloane, Apr 07 2011

Keywords

• nonn

Comments

A useful lower bound when studying certain problems involving compositions.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Crossrefs

See A201058, A201059 for numerators and denominators without ceiling. - F. Chapoton, Aug 15 2021

Programs

Magma

[Ceiling(Binomial(2*n-1,n-1)/n): n in [1..60]]; // Vincenzo Librandi, Sep 07 2016

Mathematica

Table[Ceiling[Binomial[2 n - 1, n - 1]/n], {n, 35}]  (* Harvey P. Dale, Apr 09 2011 *)