A133754 a(n) = n^5 - n^3.
0, 0, 24, 216, 960, 3000, 7560, 16464, 32256, 58320, 99000, 159720, 247104, 369096, 535080, 756000, 1044480, 1414944, 1883736, 2469240, 3192000, 4074840, 5142984, 6424176, 7948800, 9750000, 11863800, 14329224, 17188416, 20486760, 24273000, 28599360, 33521664
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..10000
- Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).
Programs
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GAP
List([0..50], n-> n^5 - n^3); # G. C. Greubel, Sep 02 2019
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Magma
[n^5-n^3: n in [0..50]]; // Vincenzo Librandi, Feb 20 2012
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Maple
seq(n^5 - n^3, n=0..50); # G. C. Greubel, Sep 02 2019
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Mathematica
Table[n^5-n^3, {n,0,50}] (* Vladimir Joseph Stephan Orlovsky, Apr 18 2011 *) -
PARI
a(n)=n^5-n^3 \\ Charles R Greathouse IV, Feb 20 2012
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Sage
[n^5 - n^3 for n in (0..50)] # G. C. Greubel, Sep 02 2019
Formula
a(n) = 12*n*(2*binomial(n+2,4)- binomial(n+1,3)). - Gary Detlefs, Mar 25 2012
Sum_{n>=2} 1/a(n) = 5/4 - zeta(3). - Daniel Suteu, Feb 06 2017
From G. C. Greubel, Sep 02 2019: (Start)
G.f.: 24*x^2*(1 + 3*x + x^2)/(1-x)^6.
E.g.f.: x^2*(12 + 24*x + 10*x^2 + x^3)*exp(x). (End)
Sum_{n>=2} (-1)^n/a(n) = 3*zeta(3)/4 + 2*log(2) - 9/4. - Amiram Eldar, Jan 09 2021