login
a(n) = (n^(n+1)-(n-1)^n) + ((n+1)^n-n^(n-1)).
2

%I #31 Sep 08 2022 08:46:12

%S 2,14,128,1504,21752,374184,7464368,169402496,4309519952,121450640200,

%T 3755499322808,126409853754144,4600799868451880,180029930424249416,

%U 7536568838736534752,336087767194699956736,15905186914751401828640,796113699641442496367496

%N a(n) = (n^(n+1)-(n-1)^n) + ((n+1)^n-n^(n-1)).

%H Daniel Suteu, <a href="/A258389/b258389.txt">Table of n, a(n) for n = 1..20</a>

%F a(n) = (n^(n+1)-(n-1)^n) + ((n+1)^n-n^(n-1)) = A084363(n) + A178922(n).

%F a(n) = A051442(n) - A051442(n-1). - _Mathew Englander_, Jul 08 2020

%e For a(3) = (3^(3+1)-(3-1)^3) + ((3+1)^3-3^(3-1)) = (3^4 - 2^3) + (4^3 - 3^2) = 128.

%t Array[#^(# + 1) - (# - 1)^# + ((# + 1)^# - #^(# - 1)) &, 20] (* _Vincenzo Librandi_, May 29 2015 *)

%o (Sidef)

%o func a(n) {

%o ((n+1)**n - n**(n-1)) -

%o ((n-1)**n - n**(n+1))

%o };

%o 1.to(Math.inf).each { |n|

%o say a(n);

%o };

%o (Magma) [(n^(n+1)-(n-1)^n) + ((n+1)^n-n^(n-1)): n in [1..20]]; // _Vincenzo Librandi_, May 29 2015

%Y Cf. A051442, A084363, A178922.

%K nonn

%O 1,1

%A _Daniel Suteu_, May 28 2015