A101709 Number of partitions of n having nonnegative even rank (the rank of a partition is the largest part minus the number of parts).

1, 0, 2, 1, 3, 2, 7, 5, 11, 10, 20, 20, 34, 35, 57, 62, 92, 104, 151, 171, 237, 274, 371, 433, 571, 670, 870, 1025, 1306, 1543, 1947, 2299, 2864, 3387, 4183, 4943, 6052, 7143, 8688, 10242, 12371, 14566, 17503, 20567, 24583, 28841, 34319, 40188, 47618, 55654, 65700, 76643, 90149, 104968

Offset

1,3

Comments

A101709(n)=A101707(n)+A047993(n). A000041(n)=2*A101707(n)+A101708(n)+A101709(n).

References

George E. Andrews, The Theory of Partitions, Addison-Wesley, Reading, Mass., 1976.

Links

Table of n, a(n) for n=1..54.

Formula

G.f.: Sum((-1)^(k+1)*x^((3*k^2-k)/2)/(1+x^k), k=1..infinity)/Product(1-x^k, k=1..infinity). - Vladeta Jovovic, Dec 20 2004

Example

a(5)=3 because the partitions of 5 with nonnegative even ranks are 5 (rank=4), 41 (rank=2) and 311 (rank=0).

Crossrefs

Cf. A000041, A101707, A101708, A047993.

Cf. A101198-A101200.

Sequence in context: A319622 A348747 A082833 * A005247 A363550 A355715

Adjacent sequences: A101706 A101707 A101708 * A101710 A101711 A101712

Keyword

nonn

Author

Emeric Deutsch, Dec 12 2004

Extensions

More terms, Joerg Arndt, Oct 07 2012

Status

approved