A168660 a(n) = n^7*(n^3 + 1)/2.
0, 1, 576, 30618, 532480, 4921875, 30373056, 141649396, 537919488, 1745783685, 5005000000, 12978455886, 30976598016, 68960620183, 144680034240, 288410625000, 549890031616, 1008202119561, 1785539723328, 3065980064770
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..10000
- Index entries for linear recurrences with constant coefficients, signature (11,-55,165,-330,462,-462,330,-165,55,-11,1).
Crossrefs
Cf. A168635.
Programs
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Magma
[n^7*(n^3+1)/2: n in [0..20]]; // Vincenzo Librandi, Aug 28 2011
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Mathematica
Table[n^7*(n^3 + 1)/2, {n,0,50}] (* G. C. Greubel, Jul 28 2016 *) -
PARI
a(n)=n^7*(n^3+1)/2 \\ Charles R Greathouse IV, Jul 29 2016
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SageMath
def A168660(n): return n^4*binomial(n^3+1,2) print([A168660(n) for n in range(31)]) # G. C. Greubel, Mar 23 2025
Formula
From G. C. Greubel, Jul 28 2016: (Start)
G.f.: x*(1 + 565*x + 24337*x^2 + 227197*x^3 + 653875*x^4 + 656479*x^5 + 227995*x^6 + 23503*x^7 + 448*x^8)/(1 - x)^11.
E.g.f.: (1/2)*x*(2 + 574*x + 9631*x^2 + 34455*x^3 + 42665*x^4 + 22848*x^5 + 5881*x^6 + 750*x^7 + 45*x^8 + x^9)*exp(x). (End)