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

2,1

Links

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

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

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

Prog

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

Crossrefs

Column 2 of A180281.

Cf. A097861, A002426.

Sequence in context: A362067 A304962 A361286 * A081154 A002900 A309087

Adjacent sequences: A180279 A180280 A180281 * A180283 A180284 A180285

Keyword

nonn

Author

R. H. Hardin, Aug 24 2010

Status

approved