|
Search: id:A116680
|
|
|
| A116680 |
|
Number of even parts in all partitions of n into distinct parts. |
|
+0
2
|
|
| 0, 0, 1, 1, 1, 2, 4, 5, 5, 8, 11, 14, 18, 23, 29, 37, 44, 55, 69, 83, 102, 124, 148, 178, 213, 253, 300, 356, 421, 494, 582, 680, 793, 926, 1074, 1246, 1446, 1668, 1922, 2215, 2545, 2918, 3345, 3823, 4366, 4982, 5668, 6445, 7321, 8300, 9401, 10639, 12021, 13566
(list; graph; listen)
|
|
|
OFFSET
|
0,6
|
|
|
COMMENT
|
a(n)=Sum(k*A116679(n,k), k>=0).
|
|
FORMULA
|
G.f.=product(1+x^j, j=1..infinity)*sum(x^(2j)/(1+x^(2j)),j=1..infinity).
|
|
EXAMPLE
|
a(9)=8 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 8 even parts.
|
|
MAPLE
|
f:=product(1+x^j, j=1..70)*sum(x^(2*j)/(1+x^(2*j)), j=1..40): fser:=series(f, x=0, 65): seq(coeff(fser, x, n), n=0..60);
|
|
CROSSREFS
|
Cf. A116679.
Adjacent sequences: A116677 A116678 A116679 this_sequence A116681 A116682 A116683
Sequence in context: A035559 A140202 A026404 this_sequence A077867 A123124 A059583
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Emeric Deutsch (deutsch(AT)duke.poly.edu), Feb 22 2006
|
|
|
Search completed in 0.002 seconds
|
