|
|
A136572
|
|
Triangle read by rows: row n consists of n zeros followed by n!.
|
|
7
|
|
|
1, 0, 1, 0, 0, 2, 0, 0, 0, 6, 0, 0, 0, 0, 24, 0, 0, 0, 0, 0, 120, 0, 0, 0, 0, 0, 0, 720, 0, 0, 0, 0, 0, 0, 0, 5040, 0, 0, 0, 0, 0, 0, 0, 0, 40320, 0, 0, 0, 0, 0, 0, 0, 0, 0, 362880, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3628800, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 39916800
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,6
|
|
COMMENTS
|
|
|
LINKS
|
|
|
FORMULA
|
Triangle, n zeros followed by n! T(n,k): n! * 0^(n-k), 0 <= k <= n.
As an infinite lower triangular matrix, A000142 (1, 1, 2, 6, 24, 120, ...) in the main diagonal and the rest zeros.
|
|
EXAMPLE
|
First few rows of the triangle:
1;
0, 1;
0, 0, 2;
0, 0, 0, 6;
0, 0, 0, 0, 24;
0, 0, 0, 0, 0, 120;
...
|
|
MATHEMATICA
|
Table[PadLeft[{n!}, n+1, 0], {n, 0, 20}]//Flatten (* Harvey P. Dale, Oct 22 2016 *)
|
|
PROG
|
(Haskell)
a136572 n k = a136572_tabl !! n !! k
a136572_row n = a136572_tabl !! n
a136572_tabl = map fst $ iterate f ([1], 1) where
f (row, i) = (0 : map (* i) row, i + 1)
|
|
CROSSREFS
|
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|