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A036291 a(n) = n*5^n.

%I A036291 #24 Sep 09 2024 16:40:19
%S A036291 0,5,50,375,2500,15625,93750,546875,3125000,17578125,97656250,
%T A036291 537109375,2929687500,15869140625,85449218750,457763671875,
%U A036291 2441406250000,12969970703125,68664550781250,362396240234375,1907348632812500,10013580322265625,52452087402343750
%N A036291 a(n) = n*5^n.
%H A036291 Vincenzo Librandi, <a href="/A036291/b036291.txt">Table of n, a(n) for n = 0..200</a>
%H A036291 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (10,-25).
%F A036291 G.f.: 5*x/(1 - 5*x)^2. - _Vincenzo Librandi_, Sep 09 2014
%F A036291 From _Amiram Eldar_, Jul 20 2020: (Start)
%F A036291 Sum_{n>=1} 1/a(n) = log(5/4).
%F A036291 Sum_{n>=1} (-1)^(n+1)/a(n) = log(6/5). (End)
%F A036291 From _Elmo R. Oliveira_, Sep 09 2024: (Start)
%F A036291 E.g.f.: 5*x*exp(5*x).
%F A036291 a(n) = n*A000351(n) = 5*A053464(n).
%F A036291 a(n) = 10*a(n-1) - 25*a(n-2) for n > 1. (End)
%p A036291 g:=1/(1-5*z): gser:=series(g, z=0, 43): seq(coeff(gser, z, n)*n, n=0..31); # _Zerinvary Lajos_, Jan 09 2009
%t A036291 Table[n 5^n, {n, 0, 20}] (* _Vincenzo Librandi_, Sep 09 2014 *)
%o A036291 (Magma) [n*5^n: n in [0..20]]; // _Vincenzo Librandi_, Sep 09 2014
%Y A036291 Cf. A000351, A053464.
%K A036291 nonn,easy
%O A036291 0,2
%A A036291 _N. J. A. Sloane_