A116156 a(n) = 5^n * n*(n + 1).
0, 10, 150, 1500, 12500, 93750, 656250, 4375000, 28125000, 175781250, 1074218750, 6445312500, 38085937500, 222167968750, 1281738281250, 7324218750000, 41503906250000, 233459472656250, 1304626464843750, 7247924804687500
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (15,-75,125).
Programs
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GAP
List([0..30], n-> 5^n*n*(n+1)); # G. C. Greubel, May 10 2019
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Magma
[(n^2+n)*5^n: n in [0..30]]; // Vincenzo Librandi, Feb 28 2013
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Magma
I:=[0,10,150]; [n le 3 select I[n] else 15*Self(n-1)-75*Self(n-2)+125*Self(n-3): n in [1..30]]; // Vincenzo Librandi, Feb 28 2013
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Mathematica
Table[(n^2 + n) 5^n, {n, 0, 30}] (* or *) CoefficientList[Series[10 x/(1 - 5 x)^3, {x, 0, 30}], x](* Vincenzo Librandi, Feb 28 2013 *) -
PARI
a(n)=(n^2+n)*5^n \\ Charles R Greathouse IV, Feb 28 2013
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Sage
[5^n*n*(n+1) for n in (0..30)] # G. C. Greubel, May 10 2019
Formula
G.f.: 10*x/(1-5*x)^3. - Vincenzo Librandi, Feb 28 2013
a(n) = 15*a(n-1) -75*a(n-2) +125*a(n-3). - Vincenzo Librandi, Feb 28 2013
a(n) = 10*A084902(n). - Bruno Berselli, Feb 28 2013
E.g.f.: 5*x*(2 + 5*x)*exp(5*x). - G. C. Greubel, May 10 2019
From Amiram Eldar, Jul 20 2020: (Start)
Sum_{n>=1} 1/a(n) = 1 - 4*log(5/4).
Sum_{n>=1} (-1)^(n+1)/a(n) = 6*log(6/5) - 1. (End)