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A258389 a(n) = (n^(n+1)-(n-1)^n) + ((n+1)^n-n^(n-1)).

%I A258389 #31 Sep 08 2022 08:46:12
%S A258389 2,14,128,1504,21752,374184,7464368,169402496,4309519952,121450640200,
%T A258389 3755499322808,126409853754144,4600799868451880,180029930424249416,
%U A258389 7536568838736534752,336087767194699956736,15905186914751401828640,796113699641442496367496
%N A258389 a(n) = (n^(n+1)-(n-1)^n) + ((n+1)^n-n^(n-1)).
%H A258389 Daniel Suteu, <a href="/A258389/b258389.txt">Table of n, a(n) for n = 1..20</a>
%F A258389 a(n) = (n^(n+1)-(n-1)^n) + ((n+1)^n-n^(n-1)) = A084363(n) + A178922(n).
%F A258389 a(n) = A051442(n) - A051442(n-1). - _Mathew Englander_, Jul 08 2020
%e A258389 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 A258389 Array[#^(# + 1) - (# - 1)^# + ((# + 1)^# - #^(# - 1)) &, 20] (* _Vincenzo Librandi_, May 29 2015 *)
%o A258389 (Sidef)
%o A258389 func a(n) {
%o A258389      ((n+1)**n - n**(n-1)) -
%o A258389      ((n-1)**n - n**(n+1))
%o A258389 };
%o A258389 1.to(Math.inf).each { |n|
%o A258389     say a(n);
%o A258389 };
%o A258389 (Magma) [(n^(n+1)-(n-1)^n) + ((n+1)^n-n^(n-1)): n in [1..20]]; // _Vincenzo Librandi_, May 29 2015
%Y A258389 Cf. A051442, A084363, A178922.
%K A258389 nonn
%O A258389 1,1
%A A258389 _Daniel Suteu_, May 28 2015