|
|
A092056
|
|
Square table by antidiagonals where T(n,k) = binomial(n+2^k-1,n).
|
|
3
|
|
|
1, 1, 1, 1, 2, 1, 1, 4, 3, 1, 1, 8, 10, 4, 1, 1, 16, 36, 20, 5, 1, 1, 32, 136, 120, 35, 6, 1, 1, 64, 528, 816, 330, 56, 7, 1, 1, 128, 2080, 5984, 3876, 792, 84, 8, 1, 1, 256, 8256, 45760, 52360, 15504, 1716, 120, 9, 1, 1, 512, 32896, 357760, 766480, 376992, 54264, 3432, 165, 10, 1
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,5
|
|
COMMENTS
|
Each column is convolution of preceding column starting from the all 1's sequence.
|
|
LINKS
|
|
|
FORMULA
|
T(n,k) = Sum_{i=0..n} T(i,k-1)*T(n-i,k-1) starting with T(n,0) = 1 for n>=0.
|
|
EXAMPLE
|
Rows start:
1, 1, 1, 1, 1, 1, 1,...
1, 2, 4, 8, 16, 32, 64,...
1, 3, 10, 36, 136, 528, 2080,...
1, 4, 20, 120, 816, 5984, 45760,...
1, 5, 35, 330, 3876, 52360, 766480,...
...
|
|
CROSSREFS
|
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|