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%I #7 Feb 11 2015 04:10:38
%S 2053230379200,18772392038400,73402986056400,257607082933200,
%T 886531102657200,2509031227903200,7078865111398080,19909183290796800,
%U 51039390957675120,128693357256063600,326570236365292920,777083694958410840,1847217791018559960,4410908197048833480
%N Number of compositions of n into exactly six different parts with distinct multiplicities.
%H Alois P. Heinz, <a href="/A246233/b246233.txt">Table of n, a(n) for n = 56..120</a>
%t $RecursionLimit = 1000; 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, 6]; Table[a[n], {n, 56, 80}] (* _Jean-François Alcover_, Feb 11 2015, after _Alois P. Heinz_ *)
%Y Column k=6 of A242896.
%K nonn
%O 56,1
%A _Alois P. Heinz_, Aug 19 2014