A180284 Number of arrangements of n indistinguishable balls in n boxes with the maximum number of balls in any box equal to 4.

4, 20, 90, 392, 1652, 6804, 27600, 110715, 440374, 1740024, 6838832, 26762645, 104356980, 405706292, 1573256772, 6087597150, 23511579564, 90659983064, 349090305487, 1342531370565, 5157512878694, 19794331541270, 75905591609120, 290857683782250, 1113774550930080

Offset: 4

Author

R. H. Hardin, Aug 24 2010

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 4..1716 (terms n = 4..59 from R. H. Hardin)

Crossrefs

Column 4 of A180281.

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))(4):
seq(a(n), n=4..30);  # Alois P. Heinz, Aug 17 2018

Mathematica

b[n_, i_, k_] := b[n, i, k] = If[n == 0, 1, If[i == 0, 0, Sum[b[n - j, i - 1, k], {j, 0, Min[n, k]}]]];
a[n_] := If[n == 0, 1, b[n, n, 4] - b[n, n, 3]];
Table[a[n], {n, 4, 30}] (* Jean-François Alcover, Aug 28 2022, after Maple program *)