A008455 - OEIS

A008455

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

0, 1, 2048, 177147, 4194304, 48828125, 362797056, 1977326743, 8589934592, 31381059609, 100000000000, 285311670611, 743008370688, 1792160394037, 4049565169664, 8649755859375, 17592186044416, 34271896307633, 64268410079232, 116490258898219, 204800000000000

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OFFSET

0,3

LINKS

T. D. Noe, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (12,-66,220,-495,792,-924,792,-495,220,-66,12,-1).

FORMULA

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

Multiplicative with a(p^e) = p^(11*e). - David W. Wilson, Aug 01 2001

Totally multiplicative with a(p) = p^11 for primes p. - Jaroslav Krizek, Nov 01 2009

From Amiram Eldar, Oct 08 2020: (Start)

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

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

From Enrique Navarrete, Feb 03 2026: (Start)

a(n) = 12*a(n-1) - 66*a(n-2) + 220*a(n-3) - 495*a(n-4) + 792*a(n-5) - 924*a(n-6) + 792*a(n-7) - 495*a(n-8) + 220*a(n-9) - 66*a(n-10) + 12*a(n-11) - a(n-12).

Dirichlet g.f.: zeta(s-11).

G.f.: x*(x^10 + 2036*x^9 + 152637*x^8 + 2203488*x^7 + 9738114*x^6 + 15724248*x^5 + 9738114*x^4 + 2203488*x^3 + 152637*x^2 + 2036*x + 1)/(1 - x)^12.

E.g.f.: x*(1 + 1023*x + 28501*x^2 + 145750*x^3 + 246730*x^4 + 179487*x^5 + 63987*x^6 + 11880*x^7 + 1155*x^8 + 55*x^9 + x^10)*exp(x). (End)

MATHEMATICA

Table[n^11, {n, 0, 30}] (* Vincenzo Librandi, Jul 05 2014 *)

PROG

(Maxima) A008455(n):=n^11$ makelist(A008455(n), n, 0, 20); /* Martin Ettl, Dec 17 2012 */

(Magma) [n^11: n in [0..40]]; // Vincenzo Librandi, Jul 05 2014

(PARI) A008455(n)=n^11 \\ M. F. Hasler, Jul 03 2025

(Python) A008455 = lambda n: n**11 # M. F. Hasler, Jul 03 2025

CROSSREFS

Partial sums are A123095.