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A107585 a(n) = 5^n - 5*n.

%I A107585 #34 Sep 10 2024 16:20:55
%S A107585 1,0,15,110,605,3100,15595,78090,390585,1953080,9765575,48828070,
%T A107585 244140565,1220703060,6103515555,30517578050,152587890545,
%U A107585 762939453040,3814697265535,19073486328030,95367431640525,476837158203020,2384185791015515,11920928955078010,59604644775390505,298023223876953000
%N A107585 a(n) = 5^n - 5*n.
%C A107585 Numbers a(n) = k such that the number m with n 5's and k 1's has digit product = digit sum = 5^n.
%H A107585 Vincenzo Librandi, <a href="/A107585/b107585.txt">Table of n, a(n) for n = 0..1000</a>
%H A107585 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (7,-11,5).
%F A107585 a(n) = 7*a(n-1) - 11*a(n-2) + 5*a(n-3), n >= 3. - _Vincenzo Librandi_, Oct 26 2011
%F A107585 G.f.: (-1-26*x^2+7*x)/((5*x-1)*(x-1)^2). - _R. J. Mathar_, Oct 26 2011
%F A107585 E.g.f.: exp(x)*(exp(4*x) - 5*x). - _Elmo R. Oliveira_, Sep 10 2024
%e A107585 Corresponding numbers m are 1, 5, 11111111111111155, ...
%t A107585 Table[5^m-5*m, {m, 0, 10}]
%t A107585 LinearRecurrence[{7,-11,5},{1,0,15},30] (* _Harvey P. Dale_, Oct 21 2015 *)
%o A107585 (Magma) [(5^n - 5*n): n in [0..25]]; // _Vincenzo Librandi_, Dec 16 2010
%o A107585 (PARI) a(n)=5^n-5*n \\ _Charles R Greathouse IV_, Oct 26 2011
%Y A107585 Cf. A107583, A107584.
%K A107585 nonn,easy
%O A107585 0,3
%A A107585 _Zak Seidov_, May 16 2005
%E A107585 Corrected by _Charles R Greathouse IV_, Sep 08 2012