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A098850
a(n) = n*(n + 18).
18
0, 19, 40, 63, 88, 115, 144, 175, 208, 243, 280, 319, 360, 403, 448, 495, 544, 595, 648, 703, 760, 819, 880, 943, 1008, 1075, 1144, 1215, 1288, 1363, 1440, 1519, 1600, 1683, 1768, 1855, 1944, 2035, 2128, 2223, 2320, 2419, 2520, 2623, 2728, 2835, 2944, 3055
OFFSET
0,2
LINKS
FORMULA
a(n) = (n+9)^2 - 9^2 = n*(n + 18), n>=0.
G.f.: x*(19 - 17*x)/(1-x)^3.
a(n) = 2*n + a(n-1) + 17 (with a(0)=0). - Vincenzo Librandi, Nov 17 2010
From G. C. Greubel, Jul 29 2016: (Start)
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).
E.g.f.: x*(19 + x)*exp(x). (End)
From Amiram Eldar, Jan 16 2021: (Start)
Sum_{n>=1} 1/a(n) = H(18)/18 = A001008(18)/A102928(18) = 14274301/73513440, where H(k) is the k-th harmonic number.
Sum_{n>=1} (-1)^(n+1)/a(n) = 1632341/44108064. (End)
MAPLE
seq(n*(n+18), n=0..52); # Emeric Deutsch, Mar 06 2005
MATHEMATICA
LinearRecurrence[{3, -3, 1}, {0, 19, 40}, 25] (* G. C. Greubel, Jul 29 2016 *)
PROG
(PARI) a(n)=n*(n+18) \\ Charles R Greathouse IV, Jun 17 2017
CROSSREFS
a(n-9), n>=10, ninth column (used for the n=9 series of the hydrogen atom) of triangle A120070.
Sequence in context: A041716 A041718 A041720 * A264537 A164078 A128677
KEYWORD
nonn,easy
AUTHOR
Eugene McDonnell (eemcd(AT)mac.com), Nov 04 2004
EXTENSIONS
More terms from Emeric Deutsch, Mar 06 2005
STATUS
approved