A282710 a(n) = binomial(2*n,n) - ceiling(4^n/(2*sqrt(n))).

0, 0, 1, 6, 23, 87, 335, 1284, 4929, 18961, 73116, 282573, 1094274, 4245403, 16498046, 64209478, 250241064, 976467300, 3814605426, 14917391732, 58391659033, 228765630254, 896981997531, 3519684170479, 13820615753489, 54304256383270, 213503120858342, 839887961545873, 3305747913345551

Offset

1,4

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 (3.1.29).

Links

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

Mathematica

Table[Binomial[2 n, n] - Ceiling[4^n / (2 Sqrt[n])], {n, 30}] (* Vincenzo Librandi, Feb 27 2017 *)

Prog

(Magma) [Binomial(2*n, n)-Ceiling(4^n/(2*Sqrt(n))): n in [1..30]]; // Vincenzo Librandi, Feb 27 2017

Crossrefs

Cf. A282708, A282709.

Sequence in context: A264690 A241394 A054491 * A295132 A013261 A013265

Adjacent sequences: A282707 A282708 A282709 * A282711 A282712 A282713

Keyword

nonn

Author

N. J. A. Sloane, Feb 26 2017

Status

approved