A016953 a(n) = (6*n + 3)^9.

19683, 387420489, 38443359375, 794280046581, 7625597484987, 46411484401953, 208728361158759, 756680642578125, 2334165173090451, 6351461955384057, 15633814156853823, 35452087835576229, 75084686279296875, 150094635296999121, 285544154243029527, 520411082988487293

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

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).

Crossrefs

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

Subsequence of A001017.

Programs

Magma

[(6*n+3)^9: n in [0..20]]; // Vincenzo Librandi, May 06 2011

Mathematica

(6*Range[0,20]+3)^9  (* Harvey P. Dale, Jan 19 2012 *)

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, Jan 19 2012

From Amiram Eldar, Mar 30 2022: (Start)

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

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

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

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