|
|
A325872
|
|
T(n, k) = [x^k] Sum_{k=0..n} Stirling1(n, k)*FallingFactorial(x, k), triangle read by rows, for n >= 0 and 0 <= k <= n.
|
|
3
|
|
|
1, 0, 1, 0, -2, 1, 0, 7, -6, 1, 0, -35, 40, -12, 1, 0, 228, -315, 130, -20, 1, 0, -1834, 2908, -1485, 320, -30, 1, 0, 17582, -30989, 18508, -5005, 665, -42, 1, 0, -195866, 375611, -253400, 81088, -13650, 1232, -56, 1, 0, 2487832, -5112570, 3805723, -1389612, 279048, -32130, 2100, -72, 1
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,5
|
|
LINKS
|
|
|
EXAMPLE
|
Triangle starts:
[0] [1]
[1] [0, 1]
[2] [0, -2, 1]
[3] [0, 7, -6, 1]
[4] [0, -35, 40, -12, 1]
[5] [0, 228, -315, 130, -20, 1]
[6] [0, -1834, 2908, -1485, 320, -30, 1]
[7] [0, 17582, -30989, 18508, -5005, 665, -42, 1]
[8] [0, -195866, 375611, -253400, 81088, -13650, 1232, -56, 1]
[9] [0, 2487832, -5112570, 3805723, -1389612, 279048, -32130, 2100, -72, 1]
|
|
MATHEMATICA
|
p[n_] := Sum[StirlingS1[n, k] FactorialPower[x, k] , {k, 0, n}];
Table[CoefficientList[FunctionExpand[p[n]], x], {n, 0, 9}] // Flatten
|
|
PROG
|
(Sage)
def a_row(n):
s = sum((-1)^(n-k)*stirling_number1(n, k)*falling_factorial(x, k) for k in (0..n))
return expand(s).list()
[a_row(n) for n in (0..9)]
|
|
CROSSREFS
|
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|