A017021 a(n) = (7*n + 3)^5.
243, 100000, 1419857, 7962624, 28629151, 79235168, 184528125, 380204032, 714924299, 1252332576, 2073071593, 3276800000, 4984209207, 7339040224, 10510100501, 14693280768, 20113571875, 27027081632, 35723051649, 46525874176
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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Magma
[(7*n+3)^5: n in [0..35]]; // Vincenzo Librandi, Jul 14 2011
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Mathematica
(7*Range[0,20]+3)^5 (* or *) LinearRecurrence[{6,-15,20,-15,6,-1},{243,100000,1419857,7962624,28629151,79235168},20] (* Harvey P. Dale, Aug 27 2017 *) -
SageMath
[(7*n+3)^5 for n in range(41)] # G. C. Greubel, Oct 17 2023
Formula
From G. C. Greubel, Oct 17 2023: (Start)
G.f.: (243 + 98542*x + 823502*x^2 + 938622*x^3 + 154907*x^4 + 1024*x^5)/(1-x)^6.
E.g.f.: (243 + 99757*x + 610050*x^2 + 667135*x^3 + 204085*x^4 + 16807*x^5)*exp(x). (End)
a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6). - Wesley Ivan Hurt, Jun 26 2025