A282709 a(n) = floor((2*n+2)^n/(n+1)!) - binomial(2*n,n).

0, 0, 0, 1, 13, 93, 569, 3225, 17498, 92473, 480626, 2471344, 12620821, 64183465, 325644870, 1650517964, 8364825118, 42417264804, 215318284778, 1094490241371, 5572229572248, 28417811854263, 145187463285629, 743117432099859, 3810434212170301, 19573513999423879, 100721431862571196

Offset

0,5

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[Floor[(2 n + 2)^n/(n + 1)!] - Binomial[2 n, n], {n, 0, 30}] (* Vincenzo Librandi, Feb 27 2017 *)

Prog

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

Crossrefs

Cf. A282708, A282710.

Sequence in context: A027670 A055608 A038742 * A005414 A044264 A044645

Adjacent sequences: A282706 A282707 A282708 * A282710 A282711 A282712

Keyword

nonn

Author

N. J. A. Sloane, Feb 26 2017

Status

approved