A019579 Place n distinguishable balls in n boxes (in n^n ways); let f(n,k) = number of ways that max in any box is k, for 1 <= k <= n; sequence gives f(n,n-2)/n.

2, 45, 160, 375, 756, 1372, 2304, 3645, 5500, 7986, 11232, 15379, 20580, 27000, 34816, 44217, 55404, 68590, 84000, 101871, 122452, 146004, 172800, 203125, 237276, 275562, 318304, 365835, 418500, 476656, 540672, 610929, 687820, 771750, 863136, 962407

Offset: 3

Author

Lee Corbin (lcorbin(AT)tsoft.com), N. J. A. Sloane

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 3..1000
• Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Crossrefs

Cf. A019576.

Programs

Mathematica

CoefficientList[Series[-(9 x^6 - 35 x^5 + 41 x^4 + 5 x^3 - 45 x^2 + 35 x + 2)/(x - 1)^5, {x, 0, 50}], x] (* Vincenzo Librandi, Oct 16 2013 *)
LinearRecurrence[{5,-10,10,-5,1},{2,45,160,375,756,1372,2304},40] (* Harvey P. Dale, Dec 18 2020 *)

Formula

a(n) = n*(n-1)^3/2, n >= 5.

G.f.: -x^3*(9*x^6 - 35*x^5 + 41*x^4 + 5*x^3 - 45*x^2 + 35*x + 2) / (x-1)^5. [Colin Barker, Jan 11 2013]

a(n) = 5*a(n-1)-10*a(n-2)+10*a(n-3)-5*a(n-4)+a(n-5). - Wesley Ivan Hurt, Dec 27 2021

Extensions

More terms from Vincenzo Librandi, Oct 16 2013