|
|
A158687
|
|
Riordan array (1/(1-x),x(1+x)^2/(1-x)).
|
|
3
|
|
|
1, 1, 1, 1, 4, 1, 1, 8, 7, 1, 1, 12, 24, 10, 1, 1, 16, 56, 49, 13, 1, 1, 20, 104, 160, 83, 16, 1, 1, 24, 168, 400, 351, 126, 19, 1, 1, 28, 248, 832, 1120, 656, 178, 22, 1, 1, 32, 344, 1520, 2912, 2561, 1102, 239, 25, 1
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,5
|
|
COMMENTS
|
Inverse of alternating signed version is A100326.
|
|
LINKS
|
|
|
FORMULA
|
Number triangle T(n,k) = Sum_{j=0..n-k} C(n-j,k)*C(2k,j).
T(n,k) = T(n-1,k) + T(n-1,k-1) + 2*T(n-2,k-1) + T(n-3,k-1), T(0,0) = T(1,0) = T(1,1) = 1, T(n,k) = 0 if k<0 or if k>n. - Philippe Deléham, Nov 11 2013
|
|
EXAMPLE
|
Number triangle begins
1,
1, 1,
1, 4, 1,
1, 8, 7, 1,
1, 12, 24, 10, 1,
1, 16, 56, 49, 13, 1,
1, 20, 104, 160, 83, 16, 1
|
|
CROSSREFS
|
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|