|
Search: id:A117409
|
|
|
| A117409 |
|
Number of partitions of n into odd parts in which the largest part occurs only once. |
|
+0
2
|
|
| 1, 0, 1, 1, 2, 2, 3, 4, 5, 6, 8, 10, 12, 15, 18, 22, 27, 32, 38, 46, 54, 64, 76, 89, 104, 122, 142, 165, 192, 222, 256, 296, 340, 390, 448, 512, 585, 668, 760, 864, 982, 1113, 1260, 1426, 1610, 1816, 2048, 2304, 2590, 2910, 3264, 3658, 4097, 4582, 5120, 5718, 6378
(list; graph; listen)
|
|
|
OFFSET
|
1,5
|
|
|
COMMENT
|
a(n)=A117408(n,1).
|
|
FORMULA
|
G.f.: Sum_{k>0} x^(2k-1)/(Product_{0<i<k} 1-x^(2i-1)).
a(n)=A000009(n-2), n>2. - Michael Somos May 28 2006
|
|
EXAMPLE
|
a(9)=5 because we have [9],[7,1,1],[5,3,1],[5,1,1,1,1] and [3,1,1,1,1,1,1].
|
|
MAPLE
|
f:=sum(x^(2*k-1)/product(1-x^(2*i-1), i=1..k-1), k=1..40): fser:=series(f, x=0, 70): seq(coeff(fser, x^n), n=1..65);
|
|
PROGRAM
|
(PARI) {a(n)=if(n<3, n==1, n-=2; polcoeff( prod(k=1, n, 1+x^k, 1+x*O(x^n)), n))} /* Michael Somos May 28 2006 */
|
|
CROSSREFS
|
Cf. A117408.
Sequence in context: A034320 A000009 A081360 this_sequence A092833 A100926 A157046
Adjacent sequences: A117406 A117407 A117408 this_sequence A117410 A117411 A117412
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Emeric Deutsch (deutsch(AT)duke.poly.edu), Mar 13 2006
|
|
|
Search completed in 0.005 seconds
|
