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a(n) = (3*n + 2)^9.
3

%I #15 Mar 31 2022 03:10:08

%S 512,1953125,134217728,2357947691,20661046784,118587876497,

%T 512000000000,1801152661463,5429503678976,14507145975869,

%U 35184372088832,78815638671875,165216101262848,327381934393961,618121839509504,1119130473102767,1953125000000000,3299763591802133

%N a(n) = (3*n + 2)^9.

%H <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (10,-45,120,-210,252,-210,120,-45,10,-1).

%F G.f.: (512 + 1948005*x + 114709518*x^2 + 1103599596*x^3 + 2887100154*x^4 + 2388954618*x^5 + 608260290*x^6 + 37732212*x^7 + 262134*x^8 + x^9)/(1 - x)^10. - _Ilya Gutkovskiy_, Jun 16 2016

%F From _Amiram Eldar_, Mar 31 2022: (Start)

%F a(n) = A016789(n)^9.

%F Sum_{n>=0} 1/a(n) = 9841*zeta(9)/19683 - 1618*Pi^9/(55801305*sqrt(3)). (End)

%t Table[(3n+2)^9,{n,0,100}] (* _Mohammad K. Azarian_, Jun 15 2016 *)

%Y Cf. A016789, A016790, A016791, A016792, A016793, A016794, A016795, A016796.

%Y Subsequence of A001017.

%K nonn,easy

%O 0,1

%A _N. J. A. Sloane_.