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A016941
a(n) = (6*n + 2)^9.
4
512, 134217728, 20661046784, 512000000000, 5429503678976, 35184372088832, 165216101262848, 618121839509504, 1953125000000000, 5416169448144896, 13537086546263552, 31087100296429568, 66540410775079424, 134217728000000000, 257327417311663616, 472161363286556672
OFFSET
0,1
LINKS
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
KEYWORD
nonn,easy
STATUS
approved