A016953 - OEIS

%I #21 Mar 30 2022 06:34:41

%S 19683,387420489,38443359375,794280046581,7625597484987,

%T 46411484401953,208728361158759,756680642578125,2334165173090451,

%U 6351461955384057,15633814156853823,35452087835576229,75084686279296875,150094635296999121,285544154243029527,520411082988487293

%N a(n) = (6*n + 3)^9.

%H Vincenzo Librandi, <a href="/A016953/b016953.txt">Table of n, a(n) for n = 0..2000</a>

%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 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_, Jan 19 2012

%F From _Amiram Eldar_, Mar 30 2022: (Start)

%F a(n) = A016945(n)^9 = A016947(n)^3.

%F a(n) = 3^9*A016761(n).

%F Sum_{n>=0} 1/a(n) = 511*zeta(9)/10077696.

%F Sum_{n>=0} (-1)^n/a(n) = 277*Pi^9/162533081088. (End)

%t (6*Range[0,20]+3)^9  (* _Harvey P. Dale_, Jan 19 2012 *)

%o (Magma) [(6*n+3)^9: n in [0..20]]; // _Vincenzo Librandi_, May 06 2011

%Y Cf. A016761, A016945, A016946, A016947, A016948, A016949, A016950, A016951, A016952.

%Y Subsequence of A001017.

%K nonn,easy

%O 0,1

%A _N. J. A. Sloane_