A008454 - OEIS

%I #43 Sep 08 2022 08:44:35

%S 0,1,1024,59049,1048576,9765625,60466176,282475249,1073741824,

%T 3486784401,10000000000,25937424601,61917364224,137858491849,

%U 289254654976,576650390625,1099511627776,2015993900449,3570467226624,6131066257801,10240000000000,16679880978201,26559922791424

%N Tenth powers: a(n) = n^10.

%C Totally multiplicative sequence with a(p) = p^10 for prime p. [_Jaroslav Krizek_, Nov 01 2009]

%C Fifth powers of the squares and the squares of fifth powers. - _Wesley Ivan Hurt_, Apr 01 2016

%H Vincenzo Librandi, <a href="/A008454/b008454.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_11">Index entries for linear recurrences with constant coefficients</a>, signature (11, -55, 165, -330, 462, -462, 330, -165, 55, -11, 1).

%F Multiplicative with a(p^e) = p^(10e). - _David W. Wilson_, Aug 01 2001

%F Totally multiplicative sequence with a(p) = p^10 for primes p. [_Jaroslav Krizek_, Nov 01 2009]

%F From _Robert Israel_, Mar 31 2016: (Start)

%F G.f.: x*(x+1)*(x^8+1012*x^7+46828*x^6+408364*x^5+901990*x^4 +408364*x^3+46828*x^2+1012*x+1)/(1-x)^11.

%F E.g.f.: x*exp(x)*(x^9+45*x^8+750*x^7+5880*x^6+22827*x^5+42525*x^4+34105*x^3+9330*x^2+511*x+1). (End)

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

%F Sum_{n>=1} 1/a(n) = zeta(10) = Pi^10/93555 (A013668).

%F Sum_{n>=1} (-1)^(n+1)/a(n) = 511*zeta(10)/512 = 73*Pi^10/6842880. (End)

%p A008454:=n->n^10; seq(A008454(n), n=0..20); # _Wesley Ivan Hurt_, Jan 22 2014

%t Table[n^10,{n,0,20}] (* _Vladimir Joseph Stephan Orlovsky_, Mar 18 2010 *)

%o (Magma) [n^10: n in [0..20]]; // _Vincenzo Librandi_, Jun 20 2011

%Y a(n) = A123867(n) + 1.

%Y Cf. A000290 (n^2), A000584 (n^5), A013668.

%K nonn,easy,mult

%O 0,3

%A _N. J. A. Sloane_