A180282 Number of arrangements of n indistinguishable balls in n boxes with the maximum number of balls in any box equal to 2.

2, 6, 18, 50, 140, 392, 1106, 3138, 8952, 25652, 73788, 212940, 616226, 1787606, 5196626, 15134930, 44152808, 128996852, 377379368, 1105350728, 3241135526, 9513228122, 27948336380, 82176836300, 241813226150, 712070156202, 2098240353906, 6186675630818

Offset: 2

Author

R. H. Hardin, Aug 24 2010

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 2..1665 (terms n=2..59 from R. H. Hardin)

Crossrefs

Column 2 of A180281.

Cf. A097861, A002426.

Programs

Maple

b:= proc(n, i, k) option remember; `if`(n=0, 1,
      `if`(i=0, 0, add(b(n-j, i-1, k), j=0..min(n, k))))
    end:
a:= n-> (k-> b(n$2, k)-b(n$2, k-1))(2):
seq(a(n), n=2..30);  # Alois P. Heinz, Aug 17 2018

PARI

for(n=2,29,print1(sum(j=1,n, binomial(n,j)*binomial(n-j,j)),", ")) \\ Hugo Pfoertner, Dec 13 2019

Formula

a(n) = Sum_{j=1..n} binomial(n,j)*binomial(n-j,j) = 2*A097861(n).

a(n) = A002426(n) - 1. - Jeppe Stig Nielsen, Dec 13 2019