A017123 a(n) = (8*n + 4)^11.

4194304, 743008370688, 204800000000000, 8293509467471872, 131621703842267136, 1196683881290399744, 7516865509350965248, 36279705600000000000, 143746751770690322432, 488595558857835544576, 1469170321634239709184, 3996373778857415671808, 10000000000000000000000

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..10000
• Index entries for linear recurrences with constant coefficients, signature (12,-66,220,-495,792,-924,792,-495,220,-66,12,-1).

Crossrefs

Cf. A013669, A016763, A016835, A017113.

Programs

Magma

[(8*n+4)^11: n in [0..15] ]; // Vincenzo Librandi, Jul 21 2011

Mathematica

(8*Range[0,20]+4)^11 (* Harvey P. Dale, Jun 11 2016 *)

Formula

G.f.: ( 4194304*(1+x)*(x^10 + 177134*x^9 + 46525293*x^8 + 1356555432*x^7 + 9480267666*x^6 + 19107752148*x^5 + 9480267666*x^4 + 1356555432*x^3 + 46525293*x^2 + 177134*x+1) ) / ( (x-1)^12 ). - R. J. Mathar, May 08 2015

From Amiram Eldar, Apr 25 2023: (Start)

a(n) = A017113(n)^11.

a(n) = 2^11*A016835(n) = 2^22*A016763(n).

Sum_{n>=0} 1/a(n) = 2047*zeta(11)/8589934592.

Sum_{n>=0} (-1)^n/a(n) = 50521*Pi^11/62342309294899200. (End)