|
Search: id:A101709
|
|
|
| A101709 |
|
Number of partitions of n having nonnegative even rank (the rank of a partition is the largest part minus the number of parts). |
|
+0
5
|
|
| 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
(list; graph; listen)
|
|
|
OFFSET
|
1,3
|
|
|
COMMENT
|
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.
|
|
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 (vladeta(AT)Eunet.yu), 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: A026805 A022477 A082833 this_sequence A005247 A135259 A122147
Adjacent sequences: A101706 A101707 A101708 this_sequence A101710 A101711 A101712
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Emeric Deutsch (deutsch(AT)duke.poly.edu), Dec 12 2004
|
|
|
Search completed in 0.002 seconds
|
