A085538 a(n) = n^5 - n^4.

0, 0, 16, 162, 768, 2500, 6480, 14406, 28672, 52488, 90000, 146410, 228096, 342732, 499408, 708750, 983040, 1336336, 1784592, 2345778, 3040000, 3889620, 4919376, 6156502, 7630848, 9375000, 11424400, 13817466, 16595712, 19803868, 23490000, 27705630, 32505856

Offset: 0

Author

N. J. A. Sloane, Jul 05 2003

Keywords

• nonn
• easy

Comments

For n >= 1, a(n) is equal to the number of functions f:{1,2,3,4,5}->{1,2,...,n} such that for a fixed x in {1,2,3,4,5} and a fixed y in {1,2,...,n} we have f(x) <> y. - Aleksandar M. Janjic and Milan Janjic, Mar 13 2007

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..10000
• Milan Janjic, Enumerative Formulas for Some Functions on Finite Sets.
• Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).

Crossrefs

A diagonal of A228273.

Cf. A000583, A000584, A146492.

Programs

Magma

[n^5-n^4: n in [0..50]]; // Vincenzo Librandi, Feb 12 2012

Maple

a:=n->sum(sum(n^3, j=1..n),k=2..n): seq(a(n), n=0..31); # Zerinvary Lajos, May 09 2007

Mathematica

Table[n^5 - n^4, {n, 0, 40}] (* or *) LinearRecurrence[{6, -15, 20, -15, 6, -1}, {0, 0, 16, 162, 768, 2500}, 40] (* Vladimir Joseph Stephan Orlovsky, Feb 20 2012 *)

PARI

a(n)=n^5-n^4 \\ Charles R Greathouse IV, Oct 07 2015

Formula

G.f.: 2*x^2*(x^3 + 18*x^2 + 33*x + 8)/(x-1)^6. - Colin Barker, Nov 06 2012

Sum_{n>=2} 1/a(n) = 4 - zeta(2) - zeta(3) - zeta(4). - Amiram Eldar, Jul 05 2020

Product_{n>=2} (1 - 1/a(n)) = A146492. - Amiram Eldar, Nov 22 2022