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 A016757 a(n) = (2*n+1)^5. 6
 1, 243, 3125, 16807, 59049, 161051, 371293, 759375, 1419857, 2476099, 4084101, 6436343, 9765625, 14348907, 20511149, 28629151, 39135393, 52521875, 69343957, 90224199, 115856201, 147008443, 184528125, 229345007, 282475249, 345025251, 418195493, 503284375, 601692057 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 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). FORMULA G.f.: (1+x)*(x^4 +236*x^3 +1446*x^2 +236*x +1)/(x-1)^6 . - R. J. Mathar, Jul 07 2017 From Amiram Eldar, Oct 10 2020: (Start) Sum_{n>=0} 1/a(n) = 31*zeta(5)/32. Sum_{n>=0} (-1)^n/a(n) = 5*Pi^5/1536 (A175571). (End) MATHEMATICA Table[(2*n+1)^5, {n, 0, 30}] (* G. C. Greubel, Sep 15 2018 *) LinearRecurrence[{6, -15, 20, -15, 6, -1}, {1, 243, 3125, 16807, 59049, 161051}, 30] (* Harvey P. Dale, Sep 04 2022 *) PROG (Magma) [(2*n+1)^5: n in [0..30]]; // Vincenzo Librandi, Sep 07 2011 (Maxima) makelist((2*n+1)^5, n, 0, 20); /* Martin Ettl, Nov 12 2012 */ (PARI) vector(30, n, n--; (2*n+1)^5) \\ G. C. Greubel, Sep 15 2018 CROSSREFS Cf. A175571. Sequence in context: A269056 A209507 A226777 * A133550 A029700 A224003 Adjacent sequences: A016754 A016755 A016756 * A016758 A016759 A016760 KEYWORD nonn,easy AUTHOR STATUS approved

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Last modified December 6 10:03 EST 2022. Contains 358630 sequences. (Running on oeis4.)