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A120071
a(n) = n*(n+20).
18
0, 21, 44, 69, 96, 125, 156, 189, 224, 261, 300, 341, 384, 429, 476, 525, 576, 629, 684, 741, 800, 861, 924, 989, 1056, 1125, 1196, 1269, 1344, 1421, 1500, 1581, 1664, 1749, 1836, 1925, 2016, 2109, 2204, 2301, 2400, 2501, 2604, 2709, 2816, 2925, 3036, 3149, 3264
OFFSET
0,2
FORMULA
a(n) = (n+10)^2 - 10^2 = n*(n+20), n>=0.
G.f.: x*(21-19*x)/(1-x)^3.
a(n) = 2*n + a(n-1) + 19 (with a(0)=0). - Vincenzo Librandi, Nov 13 2010
From Amiram Eldar, Jan 16 2021: (Start)
Sum_{n>=1} 1/a(n) = H(20)/20 = A001008(20)/A102928(20) = 11167027/62078016, where H(k) is the k-th harmonic number.
Sum_{n>=1} (-1)^(n+1)/a(n) = 155685007/4655851200. (End)
MAPLE
seq(sum(4*k-n, k=7..n), n=6..51); # Zerinvary Lajos, Feb 17 2008
MATHEMATICA
s=0; lst={}; Do[s+=n; AppendTo[lst, s], {n, 21, 6!, 2}]; lst (* Vladimir Joseph Stephan Orlovsky, Feb 26 2009 *)
PROG
(PARI) a(n)=n*(n+20) \\ Charles R Greathouse IV, Jan 21 2015
CROSSREFS
a(n-10), n>=11, tenth column (used for the n=10 series of the hydrogen atom) of triangle A120070.
For n*(n+18) see A098850.
Sequence in context: A041880 A359880 A063319 * A168519 A003857 A317210
KEYWORD
nonn,easy
AUTHOR
Wolfdieter Lang, Jul 20 2006
STATUS
approved