A016762 a(n) = (2*n + 1)^10.
1, 59049, 9765625, 282475249, 3486784401, 25937424601, 137858491849, 576650390625, 2015993900449, 6131066257801, 16679880978201, 41426511213649, 95367431640625, 205891132094649, 420707233300201, 819628286980801, 1531578985264449, 2758547353515625, 4808584372417849
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).
Programs
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Magma
[(2*n+1)^10: n in [0..20]]; // Vincenzo Librandi, Sep 07 2011
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Mathematica
(2Range[0,20]+1)^10 (* Harvey P. Dale, Nov 06 2011 *)
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PARI
for(n=0,20, print1((2*n+1)^10, ", ")) \\ G. C. Greubel, Dec 27 2016
Formula
a(n) = A016757(n)^2. - Michel Marcus, Dec 27 2016
From G. C. Greubel, Dec 27 2016: (Start)
G.f.: (1 +59038*x +9116141*x^2 +178300904*x^3 +906923282*x^4 + 1527092468*x^5 +906923282*x^6 +178300904*x^7 +9116141*x^8 +59038*x^9 + x^10)/(1-x)^11.
E.g.f.: (1 +59048*x +4823764*x^2 +42225920*x^3 +100635040*x^4 + 93590784*x^5 +40322688*x^6 +8724480*x^7 +963840*x^8 +51200*x^9 + 1024*x^10)*exp(x). (End)
Sum_{n>=0} 1/a(n) = 31*Pi^10/2903040. - Amiram Eldar, Oct 11 2020