A010801 13th powers: a(n) = n^13.
0, 1, 8192, 1594323, 67108864, 1220703125, 13060694016, 96889010407, 549755813888, 2541865828329, 10000000000000, 34522712143931, 106993205379072, 302875106592253, 793714773254144, 1946195068359375, 4503599627370496, 9904578032905937, 20822964865671168
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (14,-91,364,-1001,2002,-3003,3432,-3003,2002,-1001,364,-91,14,-1).
Crossrefs
Programs
-
Magma
[n^13: n in [0..15]]; // Vincenzo Librandi, Jun 19 2011
-
Maple
A010801 := n -> n^13; \\ M. F. Hasler, Jul 03 2025
-
Mathematica
Range[0,30]^13 (* Vladimir Joseph Stephan Orlovsky, Mar 14 2011 *)
-
PARI
A010801(n)=n^13 \\ Charles R Greathouse IV, Oct 07 2015
-
Python
A010801 = lambda n: n**13 # M. F. Hasler, Jul 03 2025
Formula
a(n) mod 10 = n mod 10. - Reinhard Zumkeller, Dec 06 2004
Totally multiplicative with a(p) = p^13 for primes p. Multiplicative with a(p^e) = p^(13*e). - Jaroslav Krizek, Nov 01 2009
G.f.: x*(x^12 + 8178*x^11 + 1479726*x^10 + 45533450*x^9 + 423281535*x^8 + 1505621508*x^7 + 2275172004*x^6 + 1505621508*x^5 + 423281535*x^4 + 45533450*x^3 + 1479726*x^2 + 8178*x + 1) / (x - 1)^14. - Colin Barker, Sep 25 2014
From Amiram Eldar, Oct 08 2020: (Start)
Sum_{n>=1} 1/a(n) = zeta(13) (A013671).
Sum_{n>=1} (-1)^(n+1)/a(n) = 4095*zeta(13)/4096. (End)