A064751 - OEIS

%I #21 Dec 23 2024 17:48:00

%S 4,49,374,2499,15624,93749,546874,3124999,17578124,97656249,537109374,

%T 2929687499,15869140624,85449218749,457763671874,2441406249999,

%U 12969970703124,68664550781249,362396240234374,1907348632812499,10013580322265624,52452087402343749

%N a(n) = n*5^n - 1.

%H Harry J. Smith, <a href="/A064751/b064751.txt">Table of n, a(n) for n = 1..150</a>

%H Paul Leyland, <a href="http://www.leyland.vispa.com/numth/factorization/cullen_woodall/cw.htm">Factors of Cullen and Woodall numbers</a>

%H Paul Leyland, <a href="http://www.leyland.vispa.com/numth/factorization/cullen_woodall/gcw.htm">Generalized Cullen and Woodall numbers</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (11,-35,25).

%F G.f.: x*(4 + 5*x - 25*x^2)/((1 - 5*x)^2*(1 - x)). - _Vincenzo Librandi_, Jun 21 2018

%F a(n) = A036291(n) - 1. - _Michel Marcus_, Jun 21 2018

%t Table[n*5^n-1,{n,20}] (* or *) LinearRecurrence[{11,-35,25},{4,49,374},20] (* _Harvey P. Dale_, Jun 25 2017 *)

%t CoefficientList[Series[(4 + 5 x - 25 x^2) / ((1 - 5 x)^2 (1 - x)), {x, 0, 33}], x] (* _Vincenzo Librandi_, Jun 21 2018 *)

%o (PARI) a(n) = { n*5^n - 1 } \\ _Harry J. Smith_, Sep 24 2009

%o (Magma) [n*5^n - 1: n in [1..30]]; // _Vincenzo Librandi_, Jun 21 2018

%Y Cf. A036291.

%K nonn

%O 1,1

%A _N. J. A. Sloane_, Oct 19 2001