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A288834
a(n) = (n+1) * 3^(n-1).
7
2, 9, 36, 135, 486, 1701, 5832, 19683, 65610, 216513, 708588, 2302911, 7440174, 23914845, 76527504, 243931419, 774840978, 2453663097, 7748409780, 24407490807, 76709256822, 240588123669, 753145430616, 2353579470675, 7343167948506, 22876792454961
OFFSET
1,1
FORMULA
O.g.f.: z*(2-3*z)/(1-3*z)^2.
a(n) = -A287768(n+1,2).
a(n) = (n+1)*A000244(n-1). - Felix Fröhlich, Jun 19 2017
a(n) = A027471(n)/3 for n >= 3. - Art Baker, Apr 12 2019
From Amiram Eldar, Jan 18 2021: (Start)
Sum_{n>=1} 1/a(n) = 9*log(3/2) - 3.
Sum_{n>=1} (-1)^(n+1)/a(n) = 3 - 9*log(4/3). (End)
MATHEMATICA
Table[(n + 1)*3^(n - 1), {n, 27}] (* Michael De Vlieger, Jun 23 2017 *)
LinearRecurrence[{6, -9}, {2, 9}, 40] (* Harvey P. Dale, Dec 16 2018 *)
PROG
(PARI) a(n) = (n+1)*3^(n-1) \\ Felix Fröhlich, Jun 19 2017
(PARI) Vec((z*(2-3*z)/(1-3*z)^2) + O(z^30)) \\ Felix Fröhlich, Jun 19 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved