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%I #11 Feb 11 2015 04:10:20
%S 60,285,498,1438,2816,5208,11195,24094,38523,85182,148051,255922,
%T 512428,991423,1573152,3318750,5820718,9712145,19523028,36637218,
%U 58805129,121712569,216006156,360123456,720094287,1340734558,2184432420,4453145090,7987036106,13417450294
%N Number of compositions of n into exactly three different parts with distinct multiplicities.
%H Alois P. Heinz and Vaclav Kotesovec, <a href="/A246230/b246230.txt">Table of n, a(n) for n = 10..220</a> (first 120 terms from Alois P. Heinz)
%t b[n_, i_, s_List] := b[n, i, s] = If[n == 0, Total[s]!, If[i<1, 0, Expand[ Sum[ If[j>0 && MemberQ[s, j], 0, If[j == 0, 1, x]*b[n-i*j, i-1, If[j == 0, s, s ~Union~{j}]]/j!], {j, 0, n/i}]]]]; a[n_] := Coefficient[b[n, n, {}], x, 3]; Table[a[n], {n, 10, 40}] (* _Jean-François Alcover_, Feb 11 2015, after _Alois P. Heinz_ *)
%Y Column k=3 of A242896.
%K nonn
%O 10,1
%A _Alois P. Heinz_, Aug 19 2014
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