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 A016925 a(n) = (6*n + 1)^5. 9
 1, 16807, 371293, 2476099, 9765625, 28629151, 69343957, 147008443, 282475249, 503284375, 844596301, 1350125107, 2073071593, 3077056399, 4437053125, 6240321451, 8587340257, 11592740743, 15386239549, 20113571875, 25937424601, 33038369407, 41615795893, 51888844699 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 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). 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) MATHEMATICA Table[(6*n + 1)^5, {n, 0, 40}] (* Amiram Eldar, Mar 28 2022 *) PROG (Magma) [(6*n+1)^5: n in [0..50]]; // Vincenzo Librandi, May 04 2011 CROSSREFS Cf. A016921, A016922, A016923, A016924, A016926. Sequence in context: A147698 A208630 A067493 * A265472 A016985 A017153 Adjacent sequences: A016922 A016923 A016924 * A016926 A016927 A016928 KEYWORD nonn,easy AUTHOR N. J. A. Sloane STATUS approved

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Last modified August 7 09:12 EDT 2024. Contains 375008 sequences. (Running on oeis4.)