|
|
A280254
|
|
Expansion of 1/(1 - Sum_{k>=1} x^p(k)), where p(k) is the number of partitions of k (A000041).
|
|
0
|
|
|
1, 1, 2, 4, 7, 14, 26, 50, 95, 180, 343, 652, 1240, 2358, 4484, 8528, 16217, 30840, 58649, 111532, 212101, 403352, 767056, 1458711, 2774031, 5275379, 10032192, 19078230, 36281088, 68995780, 131209344, 249520934, 474514204, 902384123, 1716064761, 3263442024, 6206090863, 11802129022, 22444120219
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,3
|
|
COMMENTS
|
Number of compositions (ordered partitions) into partition numbers.
|
|
LINKS
|
|
|
FORMULA
|
G.f.: 1/(1 - Sum_{k>=1} x^p(k)).
|
|
EXAMPLE
|
a(4) = 7 because we have [3, 1], [2, 2], [2, 1, 1], [1, 3], [1, 2, 1], [1, 1, 2] and [1, 1, 1, 1].
|
|
MATHEMATICA
|
nmax = 38; CoefficientList[Series[1/(1 - Sum[x^PartitionsP[k], {k, 1, nmax}]), {x, 0, nmax}], x]
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|