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A199299
a(n) = (2*n + 1)*6^n.
5
1, 18, 180, 1512, 11664, 85536, 606528, 4199040, 28553472, 191476224, 1269789696, 8344332288, 54419558400, 352638738432, 2272560758784, 14575734521856, 93096626946048, 592433080565760, 3757718396731392, 23765029860409344, 149902496042582016, 943288877536247808
OFFSET
0,2
FORMULA
a(n) = 12*a(n-1) - 36*a(n-2).
G.f.: (1+6*x)/(1-6*x)^2.
a(n) = 6*a(n-1) + 2*6^n. - Vincenzo Librandi, Nov 05 2011
From Amiram Eldar, Dec 10 2022: (Start)
Sum_{n>=0} 1/a(n) = sqrt(6)*arccoth(sqrt(6)).
Sum_{n>=0} (-1)^n/a(n) = sqrt(6)*arccot(sqrt(6)). (End)
E.g.f.: exp(6*x)*(1 + 12*x). - Stefano Spezia, May 07 2023
MATHEMATICA
a[n_] := (2*n + 1)*6^n; Array[a, 25, 0] (* Amiram Eldar, Dec 10 2022 *)
PROG
(Magma) [(2*n+1)*6^n: n in [0..30]]; // Vincenzo Librandi, Nov 05 2011
(PARI) a(n) = (2*n+1)*6^n \\ Amiram Eldar, Dec 10 2022
KEYWORD
nonn,easy
AUTHOR
Philippe Deléham, Nov 04 2011
STATUS
approved