|
| |
|
|
A100824
|
|
Number of partitions of n with at most one odd part.
|
|
1
| |
|
|
1, 1, 2, 2, 4, 3, 7, 5, 12, 7, 19, 11, 30, 15, 45, 22, 67, 30, 97, 42, 139, 56, 195, 77, 272, 101, 373, 135, 508, 176, 684, 231, 915, 297, 1212, 385, 1597, 490, 2087, 627, 2714, 792, 3506, 1002, 4508, 1255, 5763, 1575, 7338, 1958, 9296, 2436, 11732, 3010, 14742
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,3
|
|
|
FORMULA
| G.f.: (1+x/(1-x^2))/Product(1-x^(2*i), i=1..infinity). More generally, g.f. for number of partitions of n with at most k odd parts is (1+Sum(x^i/Product(1-x^(2*j), j=1..i), i=1..k))/Product(1-x^(2*i), i=1..infinity).
|
|
|
MAPLE
| seq(coeff(convert(series((1+x/(1-x^2))/mul(1-x^(2*i), i=1..100), x, 100), polynom), x, n), n=1..60); (C. Ronaldo)
|
|
|
CROSSREFS
| Cf. A000041, A000070, A008951, A000097, A000098, A000710.
Sequence in context: A057449 A007439 A096441 * A163227 A174220 A048675
Adjacent sequences: A100821 A100822 A100823 * A100825 A100826 A100827
|
|
|
KEYWORD
| easy,nonn
|
|
|
AUTHOR
| Vladeta Jovovic (vladeta(AT)eunet.rs), Jan 13 2005
|
|
|
EXTENSIONS
| More terms from C. Ronaldo (aga_new_ac(AT)hotmail.com), Jan 19 2005
|
| |
|
|
