A282708 a(n) = binomial(2*n,n) - ceiling(2^(2*n)/(n+1)).

0, 0, 0, 4, 18, 81, 338, 1384, 5588, 22405, 89430, 355906, 1413600, 5607109, 22220902, 88008656, 348435254, 1379169043, 5458320734, 21601368452, 85488832259, 338346669389, 1339221309614, 5301399720197, 20988604614673, 83106763866881, 329118546749196, 1303568050309469, 5163945978762924

Offset

0,4

Comments

a(n) >= 0.

References

P. S. Bullen, A Dictionary of Inequalities, Longman, 1998. See p. 34.

D. S. Mitrinovic, Analytic Inequalities, Springer 1970. See (3.1.28).

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Mathematica

Table[Binomial[2 n, n] - Ceiling[2^(2 n)/(n + 1)], {n, 0, 40}] (* Vincenzo Librandi, Feb 27 2017 *)

Prog

(Magma) [Binomial(2*n, n)-Ceiling(2^(2*n)/(n+1)): n in [0..30]]; // Vincenzo Librandi, Feb 27 2017

Crossrefs

Cf. A282709, A282710.

Sequence in context: A106391 A063881 A264004 * A252823 A264191 A257060

Adjacent sequences: A282705 A282706 A282707 * A282709 A282710 A282711

Keyword

nonn

Author

N. J. A. Sloane, Feb 26 2017

Status

approved