A168662 a(n) = n^7*(n^5 + 1)/2.
0, 1, 2112, 266814, 8396800, 122109375, 1088531136, 6921055372, 34360786944, 141217159725, 500005000000, 1569223931946, 4458068140032, 11649073935499, 28347008894400, 64873254375000, 140737622573056, 291311323784217, 578415996823104, 1106657906468950, 2048000640000000
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..10000
- Index entries for linear recurrences with constant coefficients, signature (13,-78,286,-715,1287,-1716,1716,-1287,715,-286,78,-13,1).
Crossrefs
Cf. A168635.
Programs
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Magma
[n^7*(n^5+1)/2: n in [0..20]]; // Vincenzo Librandi, Aug 28 2011
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Mathematica
Table[n^7 (n^5+1)/2,{n,0,20}] (* Harvey P. Dale, May 17 2016 *) -
PARI
a(n)=n^7*(n^5+1)/2 \\ Charles R Greathouse IV, Jul 29 2016
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SageMath
def A168662(n): return n^2*binomial(n^5+1,2) print([A168662(n) for n in range(31)]) # G. C. Greubel, Mar 24 2025
Formula
From G. C. Greubel, Jul 28 2016: (Start)
G.f.: x*(1 + 2099*x + 239436*x^2 + 5092668*x^3 + 33159150*x^4 + 81259650*x^5 + 81252636*x^6 + 33159324*x^7 + 5095017*x^8 + 238835*x^9 + 1984*x^10)/(1-x)^13.
E.g.f.: (1/2)*x*(2 + 2110*x + 86827*x^2 + 611851*x^3 + 1379540*x^4 + 1323673*x^5 + 627397*x^6 + 159027*x^7 + 22275*x^8 + 1705*x^9 + 66*x^10 + x^11)*exp(x). (End)