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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 5.
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%I #10 Aug 17 2018 13:50:40

%S 5,30,147,672,2970,12825,54450,228294,948090,3907995,16011905,

%T 65280800,265055772,1072443810,4326290424,17407489065,69884197635,

%U 280002750720,1119913829375,4472279679846,17834705765630,71032337773930,282586675707180,1123047360182475

%N Number of arrangements of n indistinguishable balls in n boxes with the maximum number of balls in any box equal to 5.

%H Alois P. Heinz, <a href="/A180285/b180285.txt">Table of n, a(n) for n = 5..1687</a> (terms n=5..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))(5):

%p seq(a(n), n=5..30); # _Alois P. Heinz_, Aug 17 2018

%Y Column 5 of A180281.

%K nonn

%O 5,1

%A _R. H. Hardin_, Aug 24 2010