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

%I A180284 #16 Aug 28 2022 04:18:51
%S A180284 4,20,90,392,1652,6804,27600,110715,440374,1740024,6838832,26762645,
%T A180284 104356980,405706292,1573256772,6087597150,23511579564,90659983064,
%U A180284 349090305487,1342531370565,5157512878694,19794331541270,75905591609120,290857683782250,1113774550930080
%N A180284 Number of arrangements of n indistinguishable balls in n boxes with the maximum number of balls in any box equal to 4.
%H A180284 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 A180284 b:= proc(n, i, k) option remember; `if`(n=0, 1,
%p A180284       `if`(i=0, 0, add(b(n-j, i-1, k), j=0..min(n, k))))
%p A180284     end:
%p A180284 a:= n-> (k-> b(n$2, k)-b(n$2, k-1))(4):
%p A180284 seq(a(n), n=4..30);  # _Alois P. Heinz_, Aug 17 2018
%t A180284 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 A180284 a[n_] := If[n == 0, 1, b[n, n, 4] - b[n, n, 3]];
%t A180284 Table[a[n], {n, 4, 30}] (* _Jean-François Alcover_, Aug 28 2022, after Maple program *)
%Y A180284 Column 4 of A180281.
%K A180284 nonn
%O A180284 4,1
%A A180284 _R. H. Hardin_, Aug 24 2010