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

0, 1, 1024, 59049, 1048576, 9765625, 60466176, 282475249, 1073741824, 3486784401, 10000000000, 25937424601, 61917364224, 137858491849, 289254654976, 576650390625, 1099511627776, 2015993900449, 3570467226624, 6131066257801, 10240000000000, 16679880978201, 26559922791424

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy
• mult

Comments

Fifth powers of the squares and the squares of fifth powers. - Wesley Ivan Hurt, Apr 01 2016

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (11,-55,165,-330,462,-462,330,-165,55,-11,1).

Crossrefs

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

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

Cf. A004802 - A004812 (sums of 2, ..., 12 nonzero tenth powers).

Programs

Magma

[n^10: n in [0..20]]; // Vincenzo Librandi, Jun 20 2011

Maple

A008454:=n->n^10; seq(A008454(n), n=0..20); # Wesley Ivan Hurt, Jan 22 2014

Mathematica

Table[n^10,{n,0,20}] (* Vladimir Joseph Stephan Orlovsky, Mar 18 2010 *)

PARI

A008454(n)=n^10 \\ M. F. Hasler, Jul 03 2025

Python

A008454 = lambda n: n**10 # M. F. Hasler, Jul 03 2025

Formula

Multiplicative with a(p^e) = p^(10e). - David W. Wilson, Aug 01 2001

Totally multiplicative sequence with a(p) = p^10 for primes p. - Jaroslav Krizek, Nov 01 2009

From Robert Israel, Mar 31 2016: (Start)

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.

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)

From Amiram Eldar, Oct 08 2020: (Start)

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

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