A091601 Number of compositions (ordered partitions) of n with designated summands.

1, 1, 3, 6, 14, 30, 69, 153, 345, 771, 1730, 3873, 8682, 19450, 43590, 97668, 218864, 490416, 1098933, 2462458, 5517870, 12364356, 27705944, 62083134, 139115247, 311727845, 698516370, 1565227653, 3507344882, 7859219406, 17610851898

Offset: 0

Author

Christian G. Bower, Jan 23 2004

Keywords

• nonn

Examples

			a(3)=6 because the compositions of 3 with designated summands are
3', 2'1', 1'2', 1'11, 11'1, 111'.
The composition 1121 corresponds to 1'12'1' and 11'2'1'.
		

Links

• N. J. A. Sloane, Transforms

Crossrefs

Cf. A077285.

Programs

Mathematica

Table[l = Split /@ Flatten[Permutations /@ IntegerPartitions@n, 1];
Total[Table[x = l[[i]]; Product[Length@x[[j]], {j, Length[x]}], {i, Length[l]}]], {n, 0, 15}] (* Robert Price, Jun 07 2020 *)

Formula

INVERT(DCONV(A000012, iINVERT(A000027)))

G.f.: 1/(1 - sum(k>0, x^k/(1-x^k+x^(2*k)))). - Vladeta Jovovic, Dec 04 2004