A128800 a(n) = n*(n-1)*6^n.
0, 0, 72, 1296, 15552, 155520, 1399680, 11757312, 94058496, 725594112, 5441955840, 39907676160, 287335268352, 2037468266496, 14262277865472, 98738846760960, 677066377789440, 4604051368968192, 31077346740535296, 208401031083589632, 1389340207223930880, 9213519268958699520
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (18,-108,216).
Programs
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Magma
[(n^2-n)*6^n: n in [0..25]]; // Vincenzo Librandi, Feb 11 2013
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Mathematica
CoefficientList[Series[72 x^2/(1 - 6 x)^3, {x, 0, 30}], x] (* Vincenzo Librandi, Feb 11 2013 *) LinearRecurrence[{18,-108,216},{0,0,72},30] (* Harvey P. Dale, Mar 22 2018 *)
Formula
G.f.: 72*x^2/(1 - 6*x)^3. - Vincenzo Librandi, Feb 11 2013
a(n) = 72*A081136(n). - R. J. Mathar, Apr 26 2015
a(n) = 18*a(n-1) - 108*a(n-2) + 216*a(n-3). - Wesley Ivan Hurt, Jan 20 2024
From Amiram Eldar, Apr 04 2025: (Start)
Sum_{n>=2} 1/a(n) = 1/6 - (5/6)*log(6/5).
Sum_{n>=2} (-1)^n/a(n) = (7/6)*log(7/6) - 1/6. (End)