A292884 Number of ways to shuffle together a multiset of compositions to form a composition of n.

1, 3, 8, 25, 76, 248, 806, 2714, 9205, 31846, 111185, 393224

Offset: 1

Author

Gus Wiseman, Sep 26 2017

Keywords

• nonn
• more

Examples

			The a(3)=8 shuffles are:
(111)<=((111)), (111)<=((1)(11)), (111)<=((1)(1)(1)),
(12)<=((12)), (12)<=((1)(2)),
(21)<=((21)), (21)<=((1)(2)),
(3)<=((3)).
		

Crossrefs

Cf. A034691, A059966, A060223, A269134.

Programs

Mathematica

nn=10;
comps[0]:={{}};comps[n_]:=Join@@Table[Prepend[#,i]&/@comps[n-i],{i,n}];
sps[{}]:={{}};sps[set:{i_,_}]:=Join@@Function[s,Prepend[#,s]&/@sps[Complement[set,s]]]/@Cases[Subsets[set],{i,_}];
dealings[q_]:=Union[Function[ptn,Sort[q[[#]]&/@ptn]]/@sps[Range[Length[q]]]];
Table[Total[Length/@dealings/@comps[n]],{n,nn}]

Extensions

a(12) from Robert Price, Sep 16 2018