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%I #7 Sep 16 2018 21:42:49
%S 1,3,8,25,76,248,806,2714,9205,31846,111185,393224
%N Number of ways to shuffle together a multiset of compositions to form a composition of n.
%e The a(3)=8 shuffles are:
%e (111)<=((111)), (111)<=((1)(11)), (111)<=((1)(1)(1)),
%e (12)<=((12)), (12)<=((1)(2)),
%e (21)<=((21)), (21)<=((1)(2)),
%e (3)<=((3)).
%t nn=10;
%t comps[0]:={{}};comps[n_]:=Join@@Table[Prepend[#,i]&/@comps[n-i],{i,n}];
%t sps[{}]:={{}};sps[set:{i_,___}]:=Join@@Function[s,Prepend[#,s]&/@sps[Complement[set,s]]]/@Cases[Subsets[set],{i,___}];
%t dealings[q_]:=Union[Function[ptn,Sort[q[[#]]&/@ptn]]/@sps[Range[Length[q]]]];
%t Table[Total[Length/@dealings/@comps[n]],{n,nn}]
%Y Cf. A034691, A059966, A060223, A269134.
%K nonn,more
%O 1,2
%A _Gus Wiseman_, Sep 26 2017
%E a(12) from _Robert Price_, Sep 16 2018
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