A062458 Nearest integer to (n+1)^(n+1)/n^n.

1, 4, 7, 9, 12, 15, 18, 20, 23, 26, 29, 31, 34, 37, 39, 42, 45, 48, 50, 53, 56, 58, 61, 64, 67, 69, 72, 75, 77, 80, 83, 86, 88, 91, 94, 96, 99, 102, 105, 107, 110, 113, 116, 118, 121, 124, 126, 129, 132, 135, 137, 140, 143, 145, 148, 151, 154, 156, 159, 162, 164

Offset: 0

Author

Olivier Gérard, Jun 23 2001

Keywords

• nonn
• easy
• changed

Crossrefs

Cf. A060644.

Programs

Mathematica

Join[{1},Table[Round[(1+n)^(1+n)/n^n],{n,60}]] (* Harvey P. Dale, Aug 24 2025 *)

PARI

a(n)=if(n<1,1,round(exp(1)*(n+1/2-1/24/n))) \\ Benoit Cloitre, Apr 24 2008

Formula

For n>0: a(n)=round(exp(1)*(n+1/2-1/24/n)). Coming from: (n+1)^(n+1)/n^n=exp(1)*(n+1/2-1/24/n)+O(1/n^2) - Benoit Cloitre, Apr 24 2008

Extensions

Previous Mathematica program replaced by Harvey P. Dale, Aug 24 2025