A016937 a(n) = (6*n + 2)^5.

32, 32768, 537824, 3200000, 11881376, 33554432, 79235168, 164916224, 312500000, 550731776, 916132832, 1453933568, 2219006624, 3276800000, 4704270176, 6590815232, 9039207968, 12166529024, 16105100000, 21003416576, 27027081632, 34359738368, 43204003424, 53782400000

Offset

0,1

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..2000

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). - Harvey P. Dale, Dec 13 2012

From Amiram Eldar, Mar 29 2022: (Start)

a(n) = A016933(n)^5.

a(n) = 32*A016781(n).

Sum_{n>=0} 1/a(n) = Pi^5/(11664*sqrt(3)) + 121*zeta(5)/7776. (End)

Mathematica

(6*Range[0, 20]+2)^5 (* or *) LinearRecurrence[{6, -15, 20, -15, 6, -1}, {32, 32768, 537824, 3200000, 11881376, 33554432}, 20] (* Harvey P. Dale, Dec 13 2012 *)

Prog

(Magma) [(6*n+2)^5: n in [0..30]]; // Vincenzo Librandi, May 04 2011

Crossrefs

Cf. A016781, A016933, A016934, A016935, A016936.

Sequence in context: A232596 A123393 A245291 * A074800 A320859 A285389

Adjacent sequences: A016934 A016935 A016936 * A016938 A016939 A016940

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved