|
|
A352762
|
|
Expansion of Product_{k>=1} 1 / (1 + 3^(k-1)*x^k).
|
|
4
|
|
|
1, -1, -2, -7, -11, -43, -65, -259, -146, -1798, 826, -8116, 17593, -35089, 301903, -308464, 3582403, 157367, 28816009, 9388694, 329375419, -61352008, 2991009094, 509592773, 23675224255, 1207374806, 229200996508, -129896994130, 2090952547882, -816324790165, 14079091274800
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,3
|
|
LINKS
|
|
|
FORMULA
|
a(n) = Sum_{k=0..n} (-1)^k * p(n,k) * 3^(n-k), where p(n,k) is the number of partitions of n into k parts.
|
|
MATHEMATICA
|
nmax = 30; CoefficientList[Series[Product[1/(1 + 3^(k - 1) x^k), {k, 1, nmax}], {x, 0, nmax}], x]
Table[Sum[(-1)^k Length[IntegerPartitions[n, {k}]] 3^(n - k), {k, 0, n}], {n, 0, 30}]
|
|
CROSSREFS
|
|
|
KEYWORD
|
sign
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|