A261554 Triangle read by rows: T(n,m) = number of partitions of n into at least m distinct parts, n>=1, m>=1.

1, 1, 2, 1, 2, 1, 3, 2, 4, 3, 1, 5, 4, 1, 6, 5, 2, 8, 7, 3, 10, 9, 5, 1, 12, 11, 6, 1, 15, 14, 9, 2, 18, 17, 11, 3, 22, 21, 15, 5, 27, 26, 19, 7, 1, 32, 31, 24, 10, 1, 38, 37, 29, 13, 2, 46, 45, 37, 18, 3, 54, 53, 44, 23, 5, 64, 63, 54, 30, 7, 76, 75, 65, 38, 11, 1

Offset

1,3

Comments

The n-th row has A003056(n) terms like array A008289.

References

Jacques Barbot, Essai sur la structuration de l'analyse combinatoire, Paris, Dulac, 1973, Annexe 2 p. 64.

Links

Alois P. Heinz, Rows n = 1..500, flattened

Formula

T(n,k) = Sum_{j>=k} A008289(n,j) assuming A008289(n,j)=0 when j>A003056(n)

T(n,k)-T(n,k+1) = A008289(n,k), assuming T(n,k)=0 when k>A003056(n). - Alois P. Heinz, Aug 24 2015

Example

Triangle starts:
1;
1;
2, 1;
2, 1;
3, 2;
4, 3, 1;
5, 4, 1;
6, 5, 2;
8, 7, 3;
10, 9, 5, 1;
12, 11, 6, 1;
15, 14, 9, 2;
...

Crossrefs

Cf. A008289.

Sequence in context: A139631 A029177 A321298 * A161229 A029176 A161053

Adjacent sequences: A261551 A261552 A261553 * A261555 A261556 A261557

Keyword

nonn,tabf

Author

Michel Marcus, Aug 24 2015

Extensions

More terms from Alois P. Heinz, Aug 24 2015

Status

approved