|
|
A291647
|
|
Expansion of Product_{k>=1} (1 + x^prime(k))^prime(k).
|
|
2
|
|
|
1, 0, 2, 3, 1, 11, 3, 20, 21, 20, 64, 35, 112, 117, 160, 269, 284, 477, 598, 819, 1116, 1495, 1899, 2718, 3389, 4596, 6121, 7627, 10460, 13128, 17350, 22506, 28696, 37063, 47779, 60249, 78642, 98783, 126058, 160758, 200795, 257750, 321768, 407930, 511526, 640636, 802816, 1005618, 1252820, 1567454, 1946162
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,3
|
|
COMMENTS
|
Number of partitions of n into distinct prime parts, where prime(k) different parts of size prime(k) are available (2a, 2b, 3a, 3b, 3c, ...).
|
|
LINKS
|
|
|
FORMULA
|
|
|
EXAMPLE
|
a(6) = 3 because we have [3a, 3b], [3a, 3c] and [3b, 3c].
|
|
MATHEMATICA
|
nmax = 50; CoefficientList[Series[Product[(1 + x^Prime[k])^Prime[k], {k, 1, nmax}], {x, 0, nmax}], x]
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|