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a(n) = (n+1)^n - n^(n-1) for n > 0, a(0) = 1.
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%I #28 Feb 26 2020 15:29:32

%S 1,1,7,55,561,7151,109873,1979503,40949569,956953279,24937424601,

%T 717070946087,22555076751793,770416688131663,28399211252136481,

%U 1123728578581456351,47508270371060021505,2137250367863029663487,101941438738172545000873,5138752649702088758467159

%N a(n) = (n+1)^n - n^(n-1) for n > 0, a(0) = 1.

%F a(n) = A152917(n+1) - A152917(n). - _Alexei Kourbatov_, Oct 19 2015

%F E.g.f.: W(-x) - W(-x)/(x*(1+W(-x))) where W is the Lambert W function. - _Robert Israel_, Oct 19 2015

%p a:= n-> (f-> f(n+1)-f(n))(n-> `if`(n=0, 0, n^(n-1))):

%p seq(a(n), n=0..20); # _Alois P. Heinz_, Feb 26 2020

%t Table[(n+1)^n-n^(n-1),{n,25}]

%o (Maxima) A178922[n]:=(n+1)^n-n^(n-1)$ makelist(A178922[n],n,1,30); /* _Martin Ettl_, Oct 29 2012 */

%o (PARI) vector(100, n, (n+1)^n - n^(n-1)) \\ _Altug Alkan_, Oct 19 2015

%Y Cf. A000169, A007925, A084363, A152917.

%K nonn

%O 0,3

%A _Vladimir Joseph Stephan Orlovsky_, Dec 29 2010

%E a(0)=1 prepended and definition adapted by _Alois P. Heinz_, Feb 26 2020