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A064753 a(n) = n*7^n - 1.

%I A064753 #34 May 05 2025 16:21:33
%S A064753 6,97,1028,9603,84034,705893,5764800,46118407,363182462,2824752489,
%T A064753 21750594172,166095446411,1259557135290,9495123019885,71213422649144,
%U A064753 531726889113615,3954718737782518,29311444762388081,216579008522089716,1595845325952240019,11729463145748964146
%N A064753 a(n) = n*7^n - 1.
%H A064753 Vincenzo Librandi, <a href="/A064753/b064753.txt">Table of n, a(n) for n = 1..1000</a>
%H A064753 Paul Leyland, <a href="https://web.archive.org/web/20120204131613/http://www.leyland.vispa.com/numth/factorization/cullen_woodall/cw.htm">Factors of Cullen and Woodall numbers</a>.
%H A064753 Paul Leyland, <a href="https://web.archive.org/web/20120204131629/http://www.leyland.vispa.com/numth/factorization/cullen_woodall/gcw.htm">Generalized Cullen and Woodall numbers</a>.
%H A064753 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (15,-63,49).
%F A064753 From _Alois P. Heinz_, Feb 19 2021: (Start)
%F A064753 G.f.: (56*x^2-21*x+1)/((x-1)*(7*x-1)^2).
%F A064753 a(n) = A036293(n) - 1. (End)
%F A064753 From _Elmo R. Oliveira_, May 05 2025: (Start)
%F A064753 E.g.f.: 1 + exp(x)*(7*x*exp(6*x) - 1).
%F A064753 a(n) = 15*a(n-1) - 63*a(n-2) + 49*a(n-3) for n > 3. (End)
%p A064753 k:= 7; f:= gfun:-rectoproc({1 + (k-1)*n + k*n*a(n-1) - (n-1)*a(n) = 0, a(1) = k-1}, a(n), remember): map(f, [$1..20]); # _Georg Fischer_, Feb 19 2021
%t A064753 Table[n 7^n-1,{n,20}] (* or *) LinearRecurrence[{15,-63,49},{6,97,1028},20] (* _Harvey P. Dale_, Feb 12 2022 *)
%o A064753 (Magma) [ n*7^n-1: n in [1..20]]; // _Vincenzo Librandi_, Sep 16 2011
%Y A064753 For a(n)=n*k^n-1 cf. -A000012 (k=0), A001477 (k=1), A003261 (k=2), A060352 (k=3), A060416 (k=4), A064751 (k=5), A064752 (k=6), this sequence (k=7), A064754 (k=8), A064755 (k=9), A064756 (k=10), A064757 (k=11), A064758 (k=12).
%Y A064753 Cf. A036293.
%K A064753 nonn,easy
%O A064753 1,1
%A A064753 _N. J. A. Sloane_, Oct 19 2001