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A213735
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Triangle read by rows: row n is the expansion of x^n in terms of (x+k)!/x! for decreasing k.
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1
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1, 1, -1, 1, -3, 1, 1, -6, 7, -1, 1, -10, 25, -15, 1, 1, -15, 65, -90, 31, -1, 1, -21, 140, -350, 301, -63, 1, 1, -28, 266, -1050, 1701, -966, 127, -1, 1, -36, 462, -2646, 6951, -7770, 3025, -255, 1, 1, -45, 750, -5880, 22827, -42525, 34105, -9330, 511, -1
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OFFSET
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0,5
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COMMENTS
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LINKS
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EXAMPLE
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Triangle starts
1,
1, -1,
1, -3, 1,
1, -6, 7, -1,
1, -10, 25, -15, 1,
1, -15, 65, -90, 31, -1,
...
The fourth row corresponds to the expansion
x^4 = 1 * (x + 3)! / x! - 6 * (x + 2)! / x! + 7 * (x + 1)! / x! - 1.
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PROG
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(Maxima) f1(p, n) := if n = 0 then [p] else [coeff(p, x ^ n), f1(p - expand(product(x + i, i, 1, n) * coeff(p, x^ n)), n - 1)$
f(n) := flatten(f1(x ^ n, n))$
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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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