A016747 a(n) = (2*n)^7.
0, 128, 16384, 279936, 2097152, 10000000, 35831808, 105413504, 268435456, 612220032, 1280000000, 2494357888, 4586471424, 8031810176, 13492928512, 21870000000, 34359738368, 52523350144, 78364164096, 114415582592, 163840000000, 230539333248, 319277809664, 435817657216
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..10000
- Index entries for linear recurrences with constant coefficients, signature (8,-28,56,-70,56,-28,8,-1).
Crossrefs
Cf. A016759.
Programs
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Magma
[(2*n)^7: n in [0..30]]; // Vincenzo Librandi, Sep 05 2011
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Maple
A016747:=n->(2*n)^7: seq(A016747(n), n=0..40); # Wesley Ivan Hurt, Sep 15 2018
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Mathematica
(2*Range[0,20])^7 (* Harvey P. Dale, Jan 17 2011 *)
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PARI
vector(30, n, n--; (2*n)^7) \\ G. C. Greubel, Sep 15 2018
Formula
O.g.f.: 128*x*(1 + 120*x + 1191*x^2 + 2416*x^3 + 1191*x^4 + 120*x^5 + x^6)/(1-x)^8. - R. J. Mathar, May 07 2008
From Amiram Eldar, Oct 10 2020: (Start)
Sum_{n>=1} 1/a(n) = zeta(7)/128.
Sum_{n>=1} (-1)^(n+1)/a(n) = 63*zeta(7)/8192. (End)