A016941 a(n) = (6*n + 2)^9.

512, 134217728, 20661046784, 512000000000, 5429503678976, 35184372088832, 165216101262848, 618121839509504, 1953125000000000, 5416169448144896, 13537086546263552, 31087100296429568, 66540410775079424, 134217728000000000, 257327417311663616, 472161363286556672

Offset

0,1

Links

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

Index entries for linear recurrences with constant coefficients, signature (10,-45,120,-210,252,-210,120,-45,10,-1).

Formula

a(n) = 10*a(n-1) - 45*a(n-2) + 120*a(n-3) - 210*a(n-4) + 252*a(n-5) - 210*a(n-6) + 120*a(n-7) - 45*a(n-8) + 10*a(n-9) - a(n-10). - Harvey P. Dale, Sep 21 2013

From Amiram Eldar, Mar 29 2022: (Start)

a(n) = A016933(n)^9 = A016935(n)^3.

a(n) = 2^9*A016785(n).

Sum_{n>=0} 1/a(n) = 809*Pi^9/(14285134080*sqrt(3)) + 9841*zeta(9)/10077696. (End)

Mathematica

(6*Range[0, 20]+2)^9 (* or *) LinearRecurrence[ {10, -45, 120, -210, 252, -210, 120, -45, 10, -1}, {512, 134217728, 20661046784, 512000000000, 5429503678976, 35184372088832, 165216101262848, 618121839509504, 1953125000000000, 5416169448144896}, 20] (* Harvey P. Dale, Sep 21 2013 *)

Prog

(Magma) [(6*n+2)^9: n in [0..25]]; // Vincenzo Librandi, May 05 2011

Crossrefs

Cf. A016785, A016933, A016934, A016935, A016936, A016937, A016938, A016939, A016940.

Sequence in context: A227607 A016881 A227663 * A017013 A017097 A160866

Adjacent sequences: A016938 A016939 A016940 * A016942 A016943 A016944

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved