A116165 a(n) = 7^n * n*(n+1).
0, 14, 294, 4116, 48020, 504210, 4941258, 46118408, 415065672, 3631824630, 31072277390, 261007130076, 2159240803356, 17633799894074, 142426845298290, 1139414762386320, 9039357114931472, 71184937280085342, 556917450485373558
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (21,-147,343).
Programs
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GAP
List([0..30], n-> 7^n*n*(n+1)); # G. C. Greubel, May 11 2019
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Magma
[(n^2+n)*7^n: n in [0..30]]; // Vincenzo Librandi, Feb 28 2013
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Magma
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
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Mathematica
Table[(n^2 + n) 7^n, {n, 0, 30}] (* Vincenzo Librandi, Feb 28 2013 *) -
PARI
a(n)=(n^2+n)*7^n \\ Charles R Greathouse IV, Feb 28 2013
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Sage
[7^n*n*(n+1) for n in (0..30)] # G. C. Greubel, May 11 2019
Formula
G.f.: 14*x/(1-7*x)^3. - Vincenzo Librandi, Feb 28 2013
a(n) = 21*a(n-1) - 147*a(n-2) + 343*a(n-3). - Vincenzo Librandi, Feb 28 2013
a(n+1) = 14*A027474(n+2). - Bruno Berselli, Feb 28 2013
E.g.f.: 7*x*(2 + 7*x)*exp(7*x). - G. C. Greubel, May 11 2019
From Amiram Eldar, Jul 20 2020: (Start)
Sum_{n>=1} 1/a(n) = 1 - 6*log(7/6).
Sum_{n>=1} (-1)^(n+1)/a(n) = 8*log(8/7) - 1. (End)