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A258388 a(n) = n^(n+1) + (n-1)^n.

%I A258388 #28 Nov 03 2023 15:46:45
%S A258388 1,1,9,89,1105,16649,295561,6044737,139982529,3621002129,103486784401,
%T A258388 3238428376721,110131633755793,4044369591078361,159505471943511513,
%U A258388 6723976451270702849,301716313535065716481,14358232357247077816865,722298429807405401348641
%N A258388 a(n) = n^(n+1) + (n-1)^n.
%H A258388 Alois P. Heinz, <a href="/A258388/b258388.txt">Table of n, a(n) for n = 0..350</a> (first 20 terms from Daniel Suteu)
%F A258388 From _Robert Israel_, Jun 04 2015: (Start)
%F A258388 a(n) = A007778(n-1) + A007778(n) for n>0.
%F A258388 E.g.f.: 1/(1 + W(-x))^3 - 1/(1 + W(-x))^2 - x/(W(-x)*(1+W(-x))) where W is the Lambert W function. (End)
%e A258388 a(3) = 3^(3+1) + (3-1)^3 = 3^4 + 2^3 = 81 + 8 = 89.
%p A258388 a:= n-> n^(n+1)+(n-1)^n:
%p A258388 seq(a(n), n=0..20);  # _Alois P. Heinz_, Jun 04 2015
%t A258388 Array[#^(# + 1) + (# - 1)^# &, 20] (* _Vincenzo Librandi_, May 29 2015 *)
%o A258388 (Sidef)
%o A258388 func a(n) {
%o A258388     (n-1)**n + n**(n+1)
%o A258388 };
%o A258388 1.to(Math.inf).each { |n|
%o A258388     say a(n);
%o A258388 };
%o A258388 (Magma) [n^(n+1)+(n-1)^n: n in [0..20]]; // _Vincenzo Librandi_, May 29 2015
%o A258388 (PARI) vector(10,n,n^(n+1)+(n-1)^n) \\ _Derek Orr_, Jun 01 2015
%Y A258388 Cf. A007778, A084363.
%K A258388 nonn,easy
%O A258388 0,3
%A A258388 _Daniel Suteu_, May 28 2015