|
Search: id:A118199
|
|
|
| A118199 |
|
Number of partitions of n having no parts equal to the size of their Durfee squares. |
|
+0
2
|
|
| 1, 0, 1, 1, 1, 1, 2, 3, 5, 7, 10, 13, 18, 23, 31, 40, 53, 68, 89, 113, 146, 184, 234, 293, 369, 458, 572, 706, 874, 1073, 1320, 1611, 1970, 2393, 2909, 3518, 4255, 5122, 6167, 7394, 8862, 10585, 12637, 15038, 17886, 21213, 25141, 29723, 35112, 41383, 48737, 57278
(list; graph; listen)
|
|
|
OFFSET
|
0,7
|
|
|
COMMENT
|
a(n)=A118198(n,0).
|
|
FORMULA
|
G.f.=1+sum(x^(k^2+k)/[(1-x^k)*product((1-x^i)^2, i=1..k-1)], k=1..infinity).
|
|
EXAMPLE
|
a(7)=3 because we have [7] with size of Durfee square 1, [4,3] with size of Durfee square 2 and [3,3,1] with size of Durfee square 2.
|
|
MAPLE
|
g:=1+sum(x^(k^2+k)/(1-x^k)/product((1-x^i)^2, i=1..k-1), k=1..20): gser:=series(g, x=0, 60): seq(coeff(gser, x, n), n=0..54);
|
|
CROSSREFS
|
Cf. A118198, A000041.
Sequence in context: A001401 A008628 A038499 this_sequence A088318 A038083 A060688
Adjacent sequences: A118196 A118197 A118198 this_sequence A118200 A118201 A118202
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 14 2006
|
|
|
Search completed in 0.002 seconds
|
