|
| |
|
|
A116676
|
|
Number of odd parts in all partitions of n into distinct parts.
|
|
2
| |
|
|
0, 1, 0, 2, 2, 3, 4, 5, 8, 10, 14, 16, 22, 26, 34, 43, 54, 64, 80, 96, 116, 142, 170, 202, 242, 288, 340, 404, 474, 556, 652, 762, 886, 1034, 1198, 1389, 1606, 1852, 2132, 2454, 2814, 3224, 3690, 4214, 4804, 5478, 6228, 7072, 8028, 9094, 10290, 11635, 13134
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,4
|
|
|
COMMENTS
| a(n)=Sum(k*A116675(n,k),k>=0).
|
|
|
FORMULA
| G.f.=product(1+x^j, j=1..infinity)*sum(x^(2j-1)/(1+x^(2j-1)),j=1..infinity).
|
|
|
EXAMPLE
| a(9)=10 because in the partitions of 9 into distinct parts, namely, [9],[81],[72],[6,3],[6,2,1],[5,4],[5,3,1] and [4,3,2], we have a total of 10 odd parts.
|
|
|
MAPLE
| f:=product(1+x^j, j=1..64)*sum(x^(2*j-1)/(1+x^(2*j-1)), j=1..35): fser:=series(f, x=0, 60): seq(coeff(fser, x, n), n=0..56);
|
|
|
CROSSREFS
| Cf. A116675.
Sequence in context: A175306 A021993 A186505 * A176538 A100483 A182613
Adjacent sequences: A116673 A116674 A116675 * A116677 A116678 A116679
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| Emeric Deutsch (deutsch(AT)duke.poly.edu), Feb 22 2006
|
| |
|
|
