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A325873
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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.
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2
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1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 4, 0, 1, 0, 8, 5, 10, 0, 1, 0, 26, 58, 15, 20, 0, 1, 0, 194, 217, 238, 35, 35, 0, 1, 0, 1142, 2035, 1008, 728, 70, 56, 0, 1, 0, 9736, 13470, 11611, 3444, 1848, 126, 84, 0, 1
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OFFSET
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0,13
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LINKS
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EXAMPLE
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Triangle starts:
[0] [1]
[1] [0, 1]
[2] [0, 0, 1]
[3] [0, 1, 0, 1]
[4] [0, 1, 4, 0, 1]
[5] [0, 8, 5, 10, 0, 1]
[6] [0, 26, 58, 15, 20, 0, 1]
[7] [0, 194, 217, 238, 35, 35, 0, 1]
[8] [0, 1142, 2035, 1008, 728, 70, 56, 0, 1]
[9] [0, 9736, 13470, 11611, 3444, 1848, 126, 84, 0, 1]
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MATHEMATICA
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p[n_] := Sum[Abs[StirlingS1[n, k]] FactorialPower[x, k], {k, 0, n}];
Table[CoefficientList[FunctionExpand[p[n]], x], {n, 0, 9}] // Flatten
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PROG
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(Sage)
def a_row(n):
s = sum(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)]
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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