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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, 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).
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
KEYWORD
nonn,tabl
AUTHOR
Wouter Meeussen, Feb 22 2009
STATUS
approved