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A173308
a(n) = 17*n*(n+1).
1
0, 34, 102, 204, 340, 510, 714, 952, 1224, 1530, 1870, 2244, 2652, 3094, 3570, 4080, 4624, 5202, 5814, 6460, 7140, 7854, 8602, 9384, 10200, 11050, 11934, 12852, 13804, 14790, 15810, 16864, 17952, 19074, 20230, 21420, 22644, 23902, 25194, 26520, 27880, 29274
OFFSET
0,2
FORMULA
a(n) = 34*A000217(n).
a(0)=0, a(1)=34, a(2)=102, a(n) = 3*a(n-1)-3*a(n-2)+a(n-3). G.f.: 34*x/(1-x)^3. - Colin Barker, Jan 25 2012
From Amiram Eldar, Feb 22 2023: (Start)
Sum_{n>=1} 1/a(n) = 1/17.
Sum_{n>=1} (-1)^(n+1)/a(n) = (2*log(2) - 1)/17.
Product_{n>=1} (1 - 1/a(n)) = -(17/Pi)*cos(sqrt(21/17)*Pi/2).
Product_{n>=1} (1 + 1/a(n)) = (17/Pi)*cos(sqrt(13/17)*Pi/2). (End)
MATHEMATICA
Table[17n(n+1), {n, 0, 40}] (* Harvey P. Dale, Apr 06 2011 *)
PROG
(PARI) a(n)=34*binomial(n+1, 2) \\ Charles R Greathouse IV, Jan 25 2012
(Magma) [17*n*(n+1): n in [0..50]]; // Vincenzo Librandi, Aug 20 2014
CROSSREFS
Cf. A000217.
Sequence in context: A159904 A282854 A165222 * A044285 A044666 A105088
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Feb 16 2010
EXTENSIONS
Incorrect formulas and examples deleted by R. J. Mathar, Jan 04 2011
STATUS
approved