A158900 O.g.f.:G(G(x)-1)where G(x)=Sum_k>=0,k!*x^k.

1, 1, 4, 20, 116, 756, 5448, 43032, 370704, 3472656, 35303424, 388786176, 4628774016, 59431077504, 820503839232, 12140411779584, 191844739736064, 3226219598338560, 57540789020021760, 1084906603389864960

Offset

0,3

Comments

a(n) is the number of ways to create(select) each Ferrers "type" diagram of the ORDERED partitions (compositions), then label (linearly order) the cells within each row of the diagram, and then linearly order each row.

Links

Table of n, a(n) for n=0..19.

Example

a(3)=20 because each composition of three: 3,2+1,1+2,1+1+1 can be so ordered in 3!+2!*2!+2!*2!+3!=20 ways respectively.

Mathematica

A[x_] = Sum[i! x^i, {i, 1, 20}] B[x_] = Sum[i! x^i, {i, 0, 20}] CoefficientList[Expand[Composition[B, A][x]], x]

Crossrefs

Sequence in context: A129378 A393171 A078944 * A190194 A370530 A127088

Adjacent sequences: A158897 A158898 A158899 * A158901 A158902 A158903

Keyword

nonn

Author

Geoffrey Critzer, Mar 29 2009

Status

approved