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

Author

Emeric Deutsch, Dec 12 2004

Keywords

• nonn

Comments

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

Examples

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

References

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

Crossrefs

Cf. A000041, A101707, A101708, A047993.

Cf. A101198-A101200.

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

Extensions

More terms, Joerg Arndt, Oct 07 2012