A060644 a(n) = floor((n+1)^(n+1)/n^n).

1, 4, 6, 9, 12, 14, 17, 20, 23, 25, 28, 31, 33, 36, 39, 42, 44, 47, 50, 53, 55, 58, 61, 63, 66, 69, 72, 74, 77, 80, 82, 85, 88, 91, 93, 96, 99, 101, 104, 107, 110, 112, 115, 118, 120, 123, 126, 129, 131, 134, 137, 139, 142, 145, 148, 150, 153, 156, 159, 161, 164

Offset: 0

Author

Henry Bottomley, Apr 17 2001

Keywords

• nonn

Comments

a(n) = floor(1/R) where R is the radius of convergence of the series S(x,n) = Sum_{k>=0} binomial(n*k, k)*x^k. - Michel Lagneau, Mar 09 2011

Examples

			a(7) = floor(8^8/7^7) = floor(16777216/823543) = floor(20.37...) = 20.
		

Links

• Paolo Xausa, Table of n, a(n) for n = 0..10000 (terms 0..1000 from Harry J. Smith).

Programs

Mathematica

A060644[n_] := If[n == 0, 1, Floor[(n+1)^(n+1)/n^n]]; Array[A060644, 100, 0] (* Paolo Xausa, Oct 12 2024 *)

PARI

{ for (n=0, 1000, write("b060644.txt", n, " ", floor((n + 1)^(n + 1)/n^n)); ) } \\ Harry J. Smith, Jul 09 2009

Formula

a(n) = A000312(n+1)/A000312(n) = floor(e*(n+1/2)) at least for terms shown.