|
Search: id:A102186
|
|
|
| A102186 |
|
Sum of products of multiplicities of parts in all partitions of n into odd parts. |
|
+0
1
|
|
| 1, 1, 2, 4, 5, 8, 12, 16, 22, 32, 42, 56, 76, 98, 128, 168, 213, 272, 348, 436, 548, 688, 852, 1056, 1308, 1603, 1964, 2404, 2920, 3544, 4296, 5176, 6230, 7488, 8958, 10704, 12772, 15182, 18024, 21368, 25254, 29808, 35136, 41308, 48504, 56880, 66552
(list; graph; listen)
|
|
|
OFFSET
|
0,3
|
|
|
FORMULA
|
Euler transform of period 12 sequence [1, 1, 2, 0, 1, 0, 1, 0, 2, 1, 1, 0, ...].
|
|
EXAMPLE
|
a(8)=22 because in the six partitions of 8 into odd parts, namely, 71,53,5111,3311,311111,11111111, the multiplicities of the parts are (1,1),(1,1),(1,3),(2,2),(1,5),(8) with products 1,1,3,4,5,8, having sum 22.
|
|
PROGRAM
|
(PARI) {a(n)=local(A); if(n<0, 0, A=x*O(x^n); polcoeff( eta(x^4+A)*eta(x^6+A)^2/eta(x+A)/eta(x^3+A)/eta(x^12+A), n))} /* Michael Somos Jul 30 2006 */
|
|
CROSSREFS
|
Cf. A077285.
Sequence in context: A035001 A092268 A069259 this_sequence A039842 A116901 A102829
Adjacent sequences: A102183 A102184 A102185 this_sequence A102187 A102188 A102189
|
|
KEYWORD
|
easy,nonn
|
|
AUTHOR
|
Vladeta Jovovic (vladeta(AT)Eunet.yu), Feb 16 2005
|
|
EXTENSIONS
|
More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Mar 28 2005
|
|
|
Search completed in 0.002 seconds
|
