A152917 - OEIS

%I #17 Feb 26 2020 15:27:23

%S 0,1,2,9,64,625,7776,117649,2097152,43046721,1000000000,25937424601,

%T 743008370688,23298085122481,793714773254144,29192926025390625,

%U 1152921504606846976,48661191875666868481,2185911559738696531968,104127350297911241532841

%N A000169 prefixed by an initial 0.

%C A variant of A000169, which is the main entry for this sequence. - _N. J. A. Sloane_, Dec 19 2008

%F a(n) = 0 if n = 0, otherwise a(n) = n^(n-1).

%F E.g.f.: A(x)=x*G(0) ; G(k)= 1 + x*(2*k+2)^(2*k)/((2*k+1)^(2*k) - x*(2*k+1)^(2*k)*(2*k+3)^(2*k+1)/(x*(2*k+3)^(2*k+1) + (2*k+2)^(2*k+1)/G(k+1))); (continued fraction). - _Sergei N. Gladkovskii_, Dec 30 2011

%F E.g.f.: -LambertW(-x). - _Alois P. Heinz_, Feb 26 2020

%e a(10) = 10^9 = 1000000000.

%t Join[{0},Table[n^(n-1),{n,20}]] (* _Harvey P. Dale_, Jan 28 2017 *)

%Y Cf. A000169.

%K nonn

%O 0,3

%A ShaoJun Ying (dolphinysj(AT)gmail.com), Dec 15 2008