A078111 a(n) = floor((n+2)^(n+2)/n^n).

4, 27, 64, 115, 182, 263, 359, 470, 596, 736, 891, 1061, 1246, 1445, 1660, 1889, 2132, 2391, 2664, 2953, 3256, 3573, 3906, 4253, 4615, 4992, 5384, 5790, 6211, 6647, 7098, 7563, 8044, 8539, 9049, 9573, 10113, 10667, 11236, 11820, 12418, 13031, 13659

Offset

0,1

Links

Table of n, a(n) for n=0..42.

Formula

a(n) - e^2(n+1)^2 is bounded. Conjecture: there's a constant c = 2.462... such that a(n) = floor(e^2*(n+1)^2-c).

I believe (n+2)^(n+2)/n^n = e^2(n^2 + 2n + 2/3 + o(1)), so the conjecture should be correct (with perhaps finitely many exceptions) with c = e^2/3 = 2.463.... - Charles R Greathouse IV, May 07 2013

Prog

(PARI) a(n)=(1+2./n)^n*(n+2)^2\1 \\ Charles R Greathouse IV, May 07 2013

Crossrefs

Cf. A060644.

Sequence in context: A190403 A141091 A349200 * A186882 A097792 A308474

Adjacent sequences: A078108 A078109 A078110 * A078112 A078113 A078114

Keyword

nonn

Author

Benoit Cloitre, Dec 03 2002

Status

approved