A085708 - OEIS

%I #21 Nov 12 2025 21:02:57

%S 0,7,140,2100,28000,350000,4200000,49000000,560000000,6300000000,

%T 70000000000,770000000000,8400000000000,91000000000000,

%U 980000000000000,10500000000000000,112000000000000000,1190000000000000000,12600000000000000000,133000000000000000000

%N Arithmetic derivative of 10^n.

%H Vincenzo Librandi, <a href="/A085708/b085708.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 (20,-100).

%F a(n) = 7*n*10^(n-1).

%F a(n) = A003415(A011557(n)) = A008589(n)*A011557(n-1).

%F G.f.: 7*x/(10*x-1)^2.

%F From _Elmo R. Oliveira_, Nov 12 2025: (Start)

%F E.g.f.: 7*x*exp(10*x).

%F a(n) = 20*a(n-1) - 100*a(n-2). (End)

%t Table[7*n*10^(n-1),{n,0,20}] (* _Harvey P. Dale_, Jul 09 2021 *)

%o (Magma) [7*n*10^(n-1): n in [0..20]]; // _Vincenzo Librandi_, Jun 09 2011

%Y Cf. A001787, A003415, A008589, A011557, A027471.

%K nonn,easy

%O 0,2

%A _Reinhard Zumkeller_, Jul 19 2003