|
|
A205574
|
|
Triangle T(n,k), 0<=k<=n, given by (0, 1, 1, 1, 2, 1, 3, 1, 4, 1, 5, 1, ...) DELTA (1, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938.
|
|
5
|
|
|
1, 0, 1, 0, 1, 1, 0, 2, 2, 1, 0, 5, 5, 3, 1, 0, 15, 14, 9, 4, 1, 0, 52, 44, 28, 14, 5, 1, 0, 203, 154, 93, 48, 20, 6, 1, 0, 877, 595, 333, 169, 75, 27, 7, 1, 0, 4140, 2518, 1289, 624, 280, 110, 35, 8, 1, 0, 21147, 11591, 5394, 2442, 1071, 435, 154, 44, 9, 1
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,8
|
|
COMMENTS
|
Bell convolution triangle ; g.f. for column k : (x*B(x))^k with B(x) g.f. for A000110 (Bell numbers).
Riordan array (1, x*B(x)), when B(x) the g.f. of A000110.
|
|
LINKS
|
|
|
FORMULA
|
Sum_{k=0..n} T(n,k) = A137551(n), n>0.
|
|
EXAMPLE
|
Triangle begins:
1;
0, 1;
0, 1, 1;
0, 2, 2, 1;
0, 5, 5, 3, 1;
0, 15, 14, 9, 4, 1;
0, 52, 44, 28, 14, 5, 1;
0, 203, 154, 93, 48, 20, 6, 1;
...
|
|
MAPLE
|
# Uses function PMatrix from A357368.
PMatrix(10, n -> combinat:-bell(n-1)); # Peter Luschny, Oct 19 2022
|
|
CROSSREFS
|
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|