cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A064751 a(n) = n*5^n - 1.

This page as a plain text file.
%I A064751 #25 May 06 2025 09:34:40
%S A064751 4,49,374,2499,15624,93749,546874,3124999,17578124,97656249,537109374,
%T A064751 2929687499,15869140624,85449218749,457763671874,2441406249999,
%U A064751 12969970703124,68664550781249,362396240234374,1907348632812499,10013580322265624,52452087402343749,274181365966796874
%N A064751 a(n) = n*5^n - 1.
%H A064751 Harry J. Smith, <a href="/A064751/b064751.txt">Table of n, a(n) for n = 1..150</a>
%H A064751 Paul Leyland, <a href="http://www.leyland.vispa.com/numth/factorization/cullen_woodall/cw.htm">Factors of Cullen and Woodall numbers</a>.
%H A064751 Paul Leyland, <a href="http://www.leyland.vispa.com/numth/factorization/cullen_woodall/gcw.htm">Generalized Cullen and Woodall numbers</a>.
%H A064751 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (11,-35,25).
%F A064751 G.f.: x*(4 + 5*x - 25*x^2)/((1 - 5*x)^2*(1 - x)). - _Vincenzo Librandi_, Jun 21 2018
%F A064751 a(n) = A036291(n) - 1. - _Michel Marcus_, Jun 21 2018
%F A064751 From _Elmo R. Oliveira_, May 05 2025: (Start)
%F A064751 E.g.f.: 1 + exp(x)*(5*x*exp(4*x) - 1).
%F A064751 a(n) = 11*a(n-1) - 35*a(n-2) + 25*a(n-3) for n > 3. (End)
%t A064751 Table[n*5^n-1,{n,20}] (* or *) LinearRecurrence[{11,-35,25},{4,49,374},20] (* _Harvey P. Dale_, Jun 25 2017 *)
%t A064751 CoefficientList[Series[(4 + 5 x - 25 x^2) / ((1 - 5 x)^2 (1 - x)), {x, 0, 33}], x] (* _Vincenzo Librandi_, Jun 21 2018 *)
%o A064751 (PARI) a(n) = { n*5^n - 1 } \\ _Harry J. Smith_, Sep 24 2009
%o A064751 (Magma) [n*5^n - 1: n in [1..30]]; // _Vincenzo Librandi_, Jun 21 2018
%Y A064751 Cf. A003261, A036291.
%K A064751 nonn,easy
%O A064751 1,1
%A A064751 _N. J. A. Sloane_, Oct 19 2001