A062024 a(n) = ((n+1)^n + (n-1)^n)/2.

1, 1, 5, 36, 353, 4400, 66637, 1188544, 24405761, 567108864, 14712104501, 421504185344, 13218256749601, 450353989316608, 16565151205544957, 654244800082329600, 27614800115689879553, 1240529732459024678912, 59095217374989483261925, 2975557672677668838178816

Offset: 0

Author

Amarnath Murthy, Jun 02 2001

Keywords

• nonn

Comments

Let b(n) = A302583(n) = ((n+1)^n - (n-1)^n)/2 = 0, 1, 4, 28, 272, ... then lim_{n -> infinity} b(n)/a(n) = tanh(1) = 0.76159415... . - Thomas Ordowski, Dec 06 2012

Obviously, a(n) is always odd number for even n. - Altug Alkan, Sep 28 2015

Examples

			a(3) = (4^3 + 2^3)/2 = 36.
		

Links

• Harry J. Smith, Table of n, a(n) for n = 0..100

Crossrefs

Cf. A302583.

Programs

GAP

List([0..20], n-> ((n+1)^n + (n-1)^n)/2); # G. C. Greubel, Jan 03 2020

Magma

[((n+1)^n + (n-1)^n)/2: n in [0..20]]; // Vincenzo Librandi, Sep 28 2015

Maple

A062024:=n->((n+1)^n + (n-1)^n)/2; seq(A062024(n), n=0..20); # Wesley Ivan Hurt, Nov 13 2013

Mathematica

a[n_]:=((n-1)^n+(n+1)^n)/2; a[Range[0, 20]] (* Vladimir Joseph Stephan Orlovsky, Feb 07 2010; modified by G. C. Greubel, Jan 03 2020 *)
Table[((n+1)^n + (n-1)^n)/2, {n,0,20}] (* Vincenzo Librandi, Sep 28 2015 *)

PARI

a(n) = { ((n + 1)^n + (n - 1)^n)/2 } \\ Harry J. Smith, Jul 29 2009

Sage

[((n+1)^n + (n-1)^n)/2 for n in (0..20)] # G. C. Greubel, Jan 03 2020

Formula

a(n) = n! * [x^n] exp(n*x)*cosh(x). - Ilya Gutkovskiy, Apr 10 2018

Extensions

More terms from Larry Reeves (larryr(AT)acm.org) and Jason Earls, Jun 06 2001

Offset changed from 1 to 0 by Harry J. Smith, Jul 29 2009

a(18)-a(19) from Vincenzo Librandi, Sep 28 2015