A017117 a(n) = (8*n + 4)^5.
1024, 248832, 3200000, 17210368, 60466176, 164916224, 380204032, 777600000, 1453933568, 2535525376, 4182119424, 6590815232, 10000000000, 14693280768, 21003416576, 29316250624, 40074642432, 53782400000, 71008211968, 92389579776, 118636749824, 150536645632, 188956800000
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
[(8*n+4)^5: n in [0..30] ]; // Vincenzo Librandi, Jul 21 2011
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Mathematica
(8*Range[0,20]+4)^5 (* or *) LinearRecurrence[{6,-15,20,-15,6,-1},{1024,248832,3200000,17210368,60466176,164916224},20] (* Harvey P. Dale, Nov 24 2012 *)
Formula
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); a(0)=1024, a(1)=248832, a(2)=3200000, a(3)=17210368, a(4)=60466176, a(5)=164916224. - Harvey P. Dale, Nov 24 2012
G.f.: 1024*(1+x)*(x^4 + 236*x^3 + 1446*x^2 + 236*x + 1) / (x-1)^6. - R. J. Mathar, May 08 2015
From Amiram Eldar, Apr 25 2023: (Start)
a(n) = A017113(n)^5.
Sum_{n>=0} 1/a(n) = 31*zeta(5)/32768.
Sum_{n>=0} (-1)^n/a(n) = 5*Pi^5/1572864. (End)