A359175 a(n) = binomial(2*n-2,n) - 2*(n-1).

0, 9, 48, 200, 780, 2989, 11424, 43740, 167940, 646624, 2496120, 9657674, 37442132, 145422645, 565722688, 2203961396, 8597496564, 33578000572, 131282408360, 513791607378, 2012616400036, 7890371113904, 30957699535728

Offset: 3

Author

Enrique Navarrete, Dec 27 2022

Keywords

• nonn

Comments

a(n) is the number of ways to place n indistinguishable balls into n-1 distinguishable boxes with at least one box remaining empty and not all balls placed in one box.

Examples

			For n=4, the 9 distributions are:
  |ooo|o| |
  |ooo| |o|
  |o|ooo| |
  | |ooo|o|
  |o| |ooo|
  | |o|ooo|
  |oo|oo| |
  |oo| |oo|
  | |oo|oo|.
		

Crossrefs

Cf. A001791, A350653.

Formula

a(n) = A001791(n-1) - 2*(n-1), n > 2.

G.f.: (x^4 - 2*x^3 - 2*x^2 + 2*x - 1)/(1 - x)^2 + 4*x^2/(sqrt(1 - 4*x)*(sqrt(1 - 4*x) - 1)^2). - Stefano Spezia, Dec 28 2022

D-finite with recurrence n*a(n) +7*(-n+1)*a(n-1) +2*(7*n-16)*a(n-2) +4*(-2*n+7)*a(n-3) +12*(n-5)=0. - R. J. Mathar, Jan 25 2023