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A098849
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a(n) = n*(n + 16).
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21
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0, 17, 36, 57, 80, 105, 132, 161, 192, 225, 260, 297, 336, 377, 420, 465, 512, 561, 612, 665, 720, 777, 836, 897, 960, 1025, 1092, 1161, 1232, 1305, 1380, 1457, 1536, 1617, 1700, 1785, 1872, 1961, 2052, 2145, 2240, 2337, 2436, 2537, 2640, 2745, 2852, 2961
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OFFSET
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0,2
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LINKS
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FORMULA
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a(n) = (n+8)^2 - 8^2 = n*(n + 16), n>=0.
G.f.: x*(17 - 15*x)/(1-x)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).
E.g.f.: x*(17 + x)*exp(x). (End)
Sum_{n>=1} 1/a(n) = H(16)/16 = A001008(16)/A102928(16) = 2436559/11531520, where H(k) is the k-th harmonic number.
Sum_{n>=1} (-1)^(n+1)/a(n) = 95549/2306304. (End)
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MAPLE
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MATHEMATICA
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LinearRecurrence[{3, -3, 1}, {0, 17, 36}, 50] (* G. C. Greubel, Jul 29 2016 *)
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PROG
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CROSSREFS
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a(n-8), n>=9, eighth column (used for the n=8 series of the hydrogen atom) of triangle A120070.
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KEYWORD
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nonn,easy
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AUTHOR
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Eugene McDonnell (eemcd(AT)mac.com), Nov 04 2004
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EXTENSIONS
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STATUS
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approved
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