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A054655
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Triangle T(n,k) giving coefficients in expansion of n!*binomial(x-n,n) in powers of x.
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4
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1, 1, -1, 1, -5, 6, 1, -12, 47, -60, 1, -22, 179, -638, 840, 1, -35, 485, -3325, 11274, -15120, 1, -51, 1075, -11985, 74524, -245004, 332640, 1, -70, 2086, -34300, 336049, -1961470, 6314664, -8648640, 1, -92, 3682, -83720, 1182769
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,5
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FORMULA
| n!*binomial(x-n, n)= Sum T(n, k)*x^(n-k), k=0..n.
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EXAMPLE
| 1; 1,-1; 1,-5,6; 1,-12,47,-60; ...
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MAPLE
| a054655_row := proc(n) local k; seq(coeff(expand((-1)^n*pochhammer (n-x, n)), x, n-k), k=0..n) end: [Peter Luschny, Nov 28 2010]
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PROG
| (PARI) T(n, k)=polcoeff(n!*binomial(x-n, n), n-k)
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CROSSREFS
| Cf. A054651, A054654, A008276.
Sequence in context: A131947 A195823 A105577 * A086745 A086646 A181612
Adjacent sequences: A054652 A054653 A054654 * A054656 A054657 A054658
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KEYWORD
| sign,tabl,easy,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Apr 18 2000
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