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%I #26 Sep 08 2022 08:45:24
%S 0,14,294,4116,48020,504210,4941258,46118408,415065672,3631824630,
%T 31072277390,261007130076,2159240803356,17633799894074,
%U 142426845298290,1139414762386320,9039357114931472,71184937280085342,556917450485373558
%N a(n) = 7^n * n*(n+1).
%H Vincenzo Librandi, <a href="/A116165/b116165.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (21,-147,343).
%F G.f.: 14*x/(1-7*x)^3. - _Vincenzo Librandi_, Feb 28 2013
%F a(n) = 21*a(n-1) - 147*a(n-2) + 343*a(n-3). - _Vincenzo Librandi_, Feb 28 2013
%F a(n+1) = 14*A027474(n+2). - _Bruno Berselli_, Feb 28 2013
%F E.g.f.: 7*x*(2 + 7*x)*exp(7*x). - _G. C. Greubel_, May 11 2019
%F From _Amiram Eldar_, Jul 20 2020: (Start)
%F Sum_{n>=1} 1/a(n) = 1 - 6*log(7/6).
%F Sum_{n>=1} (-1)^(n+1)/a(n) = 8*log(8/7) - 1. (End)
%t Table[(n^2 + n) 7^n, {n, 0, 30}] (* _Vincenzo Librandi_, Feb 28 2013 *)
%o (Magma) [(n^2+n)*7^n: n in [0..30]]; /* or */ I:=[0,14,294]; [n le 3 select I[n] else 21*Self(n-1)-147*Self(n-2)+343*Self(n-3): n in [1..30]]; // _Vincenzo Librandi_, Feb 28 2013
%o (PARI) a(n)=(n^2+n)*7^n \\ _Charles R Greathouse IV_, Feb 28 2013
%o (Sage) [7^n*n*(n+1) for n in (0..30)] # _G. C. Greubel_, May 11 2019
%o (GAP) List([0..30], n-> 7^n*n*(n+1)) # _G. C. Greubel_, May 11 2019
%Y Cf. A007758, A036289, A027474, A128796.
%K nonn,easy
%O 0,2
%A _Mohammad K. Azarian_, Apr 08 2007
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