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A008454 Tenth powers: a(n) = n^10.

%I A008454 #48 Jul 07 2025 00:44:56
%S A008454 0,1,1024,59049,1048576,9765625,60466176,282475249,1073741824,
%T A008454 3486784401,10000000000,25937424601,61917364224,137858491849,
%U A008454 289254654976,576650390625,1099511627776,2015993900449,3570467226624,6131066257801,10240000000000,16679880978201,26559922791424
%N A008454 Tenth powers: a(n) = n^10.
%C A008454 Fifth powers of the squares and the squares of fifth powers. - _Wesley Ivan Hurt_, Apr 01 2016
%H A008454 Vincenzo Librandi, <a href="/A008454/b008454.txt">Table of n, a(n) for n = 0..1000</a>
%H A008454 <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 A008454 Multiplicative with a(p^e) = p^(10e). - _David W. Wilson_, Aug 01 2001
%F A008454 Totally multiplicative sequence with a(p) = p^10 for primes p. - _Jaroslav Krizek_, Nov 01 2009
%F A008454 From _Robert Israel_, Mar 31 2016: (Start)
%F A008454 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 A008454 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 A008454 From _Amiram Eldar_, Oct 08 2020: (Start)
%F A008454 Sum_{n>=1} 1/a(n) = zeta(10) = Pi^10/93555 (A013668).
%F A008454 Sum_{n>=1} (-1)^(n+1)/a(n) = 511*zeta(10)/512 = 73*Pi^10/6842880. (End)
%p A008454 A008454:=n->n^10; seq(A008454(n), n=0..20); # _Wesley Ivan Hurt_, Jan 22 2014
%t A008454 Table[n^10,{n,0,20}] (* _Vladimir Joseph Stephan Orlovsky_, Mar 18 2010 *)
%o A008454 (Magma) [n^10: n in [0..20]]; // _Vincenzo Librandi_, Jun 20 2011
%o A008454 (PARI) A008454(n)=n^10 \\ _M. F. Hasler_, Jul 03 2025
%o A008454 (Python) A008454 = lambda n: n**10 # _M. F. Hasler_, Jul 03 2025
%Y A008454 a(n) = A123867(n) + 1.
%Y A008454 Cf. A000290 (n^2), A000584 (n^5), A013668.
%Y A008454 Cf. A004802 - A004812 (sums of 2, ..., 12 nonzero tenth powers).
%K A008454 nonn,easy,mult
%O A008454 0,3
%A A008454 _N. J. A. Sloane_