A008455 - OEIS

%I #34 Sep 08 2022 08:44:35

%S 0,1,2048,177147,4194304,48828125,362797056,1977326743,8589934592,

%T 31381059609,100000000000,285311670611,743008370688,1792160394037,

%U 4049565169664,8649755859375,17592186044416,34271896307633,64268410079232,116490258898219,204800000000000

%N 11th powers: a(n) = n^11.

%H T. D. Noe, <a href="/A008455/b008455.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_12">Index entries for linear recurrences with constant coefficients</a>, signature (12,-66,220,-495,792,-924,792,-495,220,-66,12,-1).

%F a(n) = A000584(n)*A001014(n).

%F Multiplicative with a(p^e) = p^(11*e). - _David W. Wilson_, Aug 01 2001

%F Totally multiplicative with a(p) = p^11 for primes p. - _Jaroslav Krizek_, Nov 01 2009

%F From _Amiram Eldar_, Oct 08 2020: (Start)

%F Sum_{n>=1} 1/a(n) = zeta(11) (A013669).

%F Sum_{n>=1} (-1)^(n+1)/a(n) = 1023*zeta(11)/1024. (End)

%t Table[n^11, {n, 0, 30}] (* _Vincenzo Librandi_, Jul 05 2014 *)

%o (Maxima) A008455(n):=n^11$ makelist(A008455(n),n,0,20); /* _Martin Ettl_, Dec 17 2012 */

%o (Magma) [n^11: n in [0..40]]; // _Vincenzo Librandi_, Jul 05 2014

%Y Cf. A000583, A000584, A001014, A001017, A008454, A013669.

%K nonn,easy,mult

%O 0,3

%A _N. J. A. Sloane_.