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

0,1

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

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.

a(n) = 2^5*A016829(n) = 2^10*A016757(n).

Sum_{n>=0} 1/a(n) = 31*zeta(5)/32768.

Sum_{n>=0} (-1)^n/a(n) = 5*Pi^5/1572864. (End)

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 *)

Prog

(Magma) [(8*n+4)^5: n in [0..30] ]; // Vincenzo Librandi, Jul 21 2011

Crossrefs

Cf. A013663, A016757, A016829, A017113.

Sequence in context: A224284 A224207 A017033 * A269293 A017213 A221092

Adjacent sequences: A017114 A017115 A017116 * A017118 A017119 A017120

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved