A016925 a(n) = (6*n + 1)^5.
1, 16807, 371293, 2476099, 9765625, 28629151, 69343957, 147008443, 282475249, 503284375, 844596301, 1350125107, 2073071593, 3077056399, 4437053125, 6240321451, 8587340257, 11592740743, 15386239549, 20113571875, 25937424601, 33038369407, 41615795893, 51888844699
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..2000
- Marián Štofka, Problem 11715, The American Mathematical Monthly, Vol. 120, No. 6 (2013), p. 569; An Infinite Sum Introduces a Zeta, Solution to Problem 11715 by Michael Hoffman, ibid., Vol. 122, No. 6 (2015), pp. 608-609.
- Roberto Tauraso, Problem 11715.
- Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).
Programs
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Magma
[(6*n+1)^5: n in [0..50]]; // Vincenzo Librandi, May 04 2011
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Mathematica
Table[(6*n + 1)^5, {n, 0, 40}] (* Amiram Eldar, Mar 28 2022 *)
Formula
From Amiram Eldar, Mar 28 2022: (Start)
a(n) = A016921(n)^5.
Sum_{n>=0} 1/a(n) = ((1-1/2^5)*(1-1/3^5)*zeta(5) + 11*(Pi/3)^5/(8*sqrt(3)))/2 (Štofka, 2013). (End)