A201059 -id:A201059 - cp's OEIS frontend

A201058 Numerator of binomial(2n,n)/(2n).

1, 3, 10, 35, 126, 77, 1716, 6435, 24310, 46189, 352716, 676039, 5200300, 10029150, 5170584, 300540195, 1166803110, 756261275, 17672631900, 6892326441, 89709645740, 526024740930, 4116715363800, 2687300306925, 63205303218876, 123979633237026, 973469712824056, 136583760727865, 15033633249770520, 29566145391215356

Offset: 1

N. J. A. Sloane, Nov 26 2011

There is at least one published paper that refers to binomial(2n,n)/(2n) as the Catalan numbers. Of course the Catalan numbers are really A000108.

			1, 3/2, 10/3, 35/4, 126/5, 77, 1716/7, 6435/8, 24310/9, 46189/5, 352716/11, 676039/6, ...

Patrick Dehornoy, On the rotation distance between binary trees, Adv. Math. 223 (2010), no. 4, 1316-1355.

Cf. A000108, A201059.

Numerator[Table[Binomial[2n,n]/(2n),{n,30}]] (* Harvey P. Dale, Jan 06 2013 *)

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

Original entry on oeis.org

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

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

nonn

A useful lower bound when studying certain problems involving compositions.

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

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

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

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

cp's OEIS Frontend

A201058 Numerator of binomial(2n,n)/(2n).

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