A157045 Triangular table: number of partitions of n into exactly n-k parts, each <= n-k. Same as A157044 but with rows reversed.

1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 2, 0, 0, 1, 1, 2, 2, 0, 0, 1, 1, 2, 3, 2, 0, 0, 1, 1, 2, 3, 4, 1, 0, 0, 1, 1, 2, 3, 5, 4, 1, 0, 0, 1, 1, 2, 3, 5, 6, 5, 0, 0, 0, 1, 1, 2, 3, 5, 7, 8, 4, 0, 0, 0, 1, 1, 2, 3, 5, 7, 10, 9, 4, 0, 0, 0, 1, 1, 2, 3, 5, 7, 11, 12, 11, 3, 0, 0, 0, 1, 1, 2, 3, 5, 7, 11, 14, 16, 11

Offset: 1

Author

Wouter Meeussen, Feb 22 2009

Keywords

• nonn
• tabl

Comments

See A157044. Rows approach the partition numbers.

References

• George E. Andrews, The Theory of Partitions, Addison-Wesley, Reading, Mass., 1976 (Theorem 1.5).

Crossrefs

Cf. A000041, A157044, A157046, A047993

Programs

Mathematica

Table[T[n-1,n-k,n-k+2]-T[n-1,n-k-1,n-k+2],{n,1,9},{k,1,n}] with T[n,a,b] as defined in A047993.