%I
%S 37837800,290089800,913512600,2870988120,8647198560,20798177400,
%T 52611741000,134182896120,299814913440,688027838400,1598171790600,
%U 3415039782840,7488313184520,16753428299160,34973088459120,74787505653264,162128661286152,333915200009352
%N Number of compositions of n into exactly five different parts with distinct multiplicities.
%H Alois P. Heinz, <a href="/A246232/b246232.txt">Table of n, a(n) for n = 35..120</a>
%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[ni*j, i1, If[j == 0, s, s ~Union~ {j}]]/j!], {j, 0, n/i}]]]]; a[n_] := Coefficient[b[n, n, {}], x, 5]; Table[a[n], {n, 35, 60}] (* _JeanFrançois Alcover_, Feb 11 2015, after _Alois P. Heinz_ *)
%Y Column k=5 of A242896.
%K nonn
%O 35,1
%A _Alois P. Heinz_, Aug 19 2014
