|
|
A026836
|
|
Triangular array T read by rows: T(n,k) = number of partitions of n into distinct parts, the greatest being k, for k=1,2,...,n.
|
|
6
|
|
|
1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 0, 2, 1, 1, 1, 0, 0, 0, 1, 2, 1, 1, 1, 0, 0, 0, 1, 2, 2, 1, 1, 1, 0, 0, 0, 1, 2, 2, 2, 1, 1, 1, 0, 0, 0, 0, 2, 3, 2, 2, 1, 1, 1, 0, 0, 0, 0, 2, 3, 3, 2, 2, 1, 1, 1, 0, 0, 0, 0, 1, 3, 4, 3, 2, 2, 1, 1
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,25
|
|
COMMENTS
|
|
|
LINKS
|
|
|
FORMULA
|
T(n, k) = coefficient of x^n in x^k*Product_{i=1..k-1} (1+x^i). - Vladeta Jovovic, Aug 07 2003
|
|
EXAMPLE
|
Triangle begins:
[1]
[0, 1]
[0, 1, 1]
[0, 0, 1, 1]
[0, 0, 1, 1, 1]
[0, 0, 1, 1, 1, 1]
[0, 0, 0, 2, 1, 1, 1]
[0, 0, 0, 1, 2, 1, 1, 1]
[0, 0, 0, 1, 2, 2, 1, 1, 1]
[0, 0, 0, 1, 2, 2, 2, 1, 1, 1]
[0, 0, 0, 0, 2, 3, 2, 2, 1, 1, 1]
[0, 0, 0, 0, 2, 3, 3, 2, 2, 1, 1, 1]
[0, 0, 0, 0, 1, 3, 4, 3, 2, 2, 1, 1, 1]
[0, 0, 0, 0, 1, 3, 4, 4, 3, 2, 2, 1, 1, 1]
|
|
MAPLE
|
with(combinat);
f2:=proc(n) local i, j, p, t0, t1, t2;
t0:=Array(1..n, 0);
t1:=partition(n);
p:=numbpart(n);
for i from 1 to p do
t2:=t1[i];
if nops(convert(t2, set))=nops(t2) then
# now have a partition t2 of n into distinct parts
t0[t2[-1]]:=t0[t2[-1]]+1;
od:
[seq(t0[j], j=1..n)];
end proc;
|
|
CROSSREFS
|
If seen as a square array then transpose of A070936 and visible form of A053632. Central diagonal and those to the right of center are A000009 as are row sums.
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|