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Number of arrangements of n indistinguishable balls in n boxes with the maximum number of balls in any box equal to 4.
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%I #16 Aug 28 2022 04:18:51

%S 4,20,90,392,1652,6804,27600,110715,440374,1740024,6838832,26762645,

%T 104356980,405706292,1573256772,6087597150,23511579564,90659983064,

%U 349090305487,1342531370565,5157512878694,19794331541270,75905591609120,290857683782250,1113774550930080

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

%H Alois P. Heinz, <a href="/A180284/b180284.txt">Table of n, a(n) for n = 4..1716</a> (terms n = 4..59 from R. H. Hardin)

%p b:= proc(n, i, k) option remember; `if`(n=0, 1,

%p `if`(i=0, 0, add(b(n-j, i-1, k), j=0..min(n, k))))

%p end:

%p a:= n-> (k-> b(n$2, k)-b(n$2, k-1))(4):

%p seq(a(n), n=4..30); # _Alois P. Heinz_, Aug 17 2018

%t 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]}]]];

%t a[n_] := If[n == 0, 1, b[n, n, 4] - b[n, n, 3]];

%t Table[a[n], {n, 4, 30}] (* _Jean-François Alcover_, Aug 28 2022, after Maple program *)

%Y Column 4 of A180281.

%K nonn

%O 4,1

%A _R. H. Hardin_, Aug 24 2010