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%I #17 Sep 08 2022 08:46:06
%S 0,6,108,1458,17496,196830,2125764,22320522,229582512,2324522934,
%T 23245229340,230127770466,2259436291848,22029503845518,
%U 213516729579636,2058911320946490,19765548681086304,189008059262887782,1801135623563989452,17110788423857899794
%N a(n) = 2*n*3^(2*n-1).
%C Arithmetic derivative of 9^n: a(n) = A003415(9^n).
%C Sum of reciprocals of a(n), for n>0: (3/2)*log(9/8).
%H Bruno Berselli, <a href="/A230540/b230540.txt">Table of n, a(n) for n = 0..100</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (18,-81).
%F G.f.: 6*x/(1-9*x)^2.
%F a(n) = 6*A053540(n), with A053540(0)=0.
%t Table[2 n 3^(2 n - 1), {n, 0, 20}]
%o (Magma) [2*n*3^(2*n-1): n in [0..20]];
%o (PARI) a(n) = 2*n*3^(2*n-1); \\ _Michel Marcus_, Oct 23 2013
%Y Cf. A001019, A003415.
%Y Cf. arithmetic derivative of k^n: A001787 (k=2), A027471 (k=3), A018215 (k=4), A053464 (k=5), A212700 (k=6), A027473 (k=7), A230539 (k=8), this sequence, A085708 (k=10), A081127 (k=11).
%K nonn,easy
%O 0,2
%A _Bruno Berselli_, Oct 23 2013