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

1,13

Comments

See A157044. Rows approach the partition numbers.

References

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

Links

Table of n, a(n) for n=1..101.

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.

Crossrefs

Cf. A000041, A157044, A157046, A047993

Sequence in context: A241069 A261084 A035144 * A035208 A025881 A039804

Adjacent sequences: A157042 A157043 A157044 * A157046 A157047 A157048

Keyword

nonn,tabl

Author

Wouter Meeussen, Feb 22 2009

Status

approved