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A163758
a(n) = 9*n*(n+1).
3
0, 18, 54, 108, 180, 270, 378, 504, 648, 810, 990, 1188, 1404, 1638, 1890, 2160, 2448, 2754, 3078, 3420, 3780, 4158, 4554, 4968, 5400, 5850, 6318, 6804, 7308, 7830, 8370, 8928, 9504, 10098, 10710, 11340, 11988, 12654, 13338, 14040, 14760, 15498, 16254, 17028
OFFSET
0,2
COMMENTS
18 times the n-th triangular number.
Numbers of the form 36*m^2 + 18*m, where m = 0,-1,1,-2,2,-3,3,... - Bruno Berselli, Apr 07 2013
FORMULA
G.f.: 18*x/(1-x)^3.
a(n) = 18*A000217(n) = 9*A002378(n).
E.g.f.: 9*x*(x + 2)*exp(x). - G. C. Greubel, Aug 02 2017
From Amiram Eldar, Feb 22 2023: (Start)
Sum_{n>=1} 1/a(n) = 1/9.
Sum_{n>=1} (-1)^(n+1)/a(n) = (2*log(2) - 1)/9.
Product_{n>=1} (1 - 1/a(n)) = -(9/Pi)*cos(sqrt(13)*Pi/6).
Product_{n>=1} (1 + 1/a(n)) = (9/Pi)*cos(sqrt(5)*Pi/6). (End)
MATHEMATICA
Table[9 n (n + 1), {n, 0, 100}] (* Vladimir Joseph Stephan Orlovsky, Jun 26 2011 *)
PROG
(Magma) [0] cat [36*m^2+18*m where m is n*t: t in [-1, 1], n in [1..20]]; // Bruno Berselli, Apr 07 2013
(PARI) a(n)=9*n*(n+1) \\ Charles R Greathouse IV, Jun 17 2017
CROSSREFS
Sequence in context: A044120 A056808 A044501 * A232546 A069973 A272138
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Aug 03 2009
EXTENSIONS
a(35) inserted by R. J. Mathar, Aug 06 2009
STATUS
approved