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A142070 Triangle T(n,k) read by rows: the coefficient [x^k] of the polynomial Product_{i=1..n} (i+1)*x-i in row n>=0 and column 0<=k<=n. 1
1, -1, 2, 2, -7, 6, -6, 29, -46, 24, 24, -146, 329, -326, 120, -120, 874, -2521, 3604, -2556, 720, 720, -6084, 21244, -39271, 40564, -22212, 5040, -5040, 48348, -197380, 444849, -598116, 479996, -212976, 40320, 40320, -432144, 2014172, -5335212, 8788569, -9223012, 6023772, -2239344, 362880 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Row sums are one.

This is essentially a signed version of A088996. - Peter Bala, Jan 09 2017

LINKS

Table of n, a(n) for n=0..44.

EXAMPLE

1;

-1, 2;

2, -7, 6;

-6, 29, -46, 24;

24, -146, 329, -326, 120;

-120, 874, -2521, 3604, -2556, 720;

720, -6084, 21244, -39271, 40564, -22212, 5040;

-5040,48348, -197380, 444849, -598116, 479996, -212976, 40320;

40320, -432144, 2014172, -5335212,8788569, -9223012, 6023772, -2239344, 362880;

...

MAPLE

A142070 := proc(n, k)

    local x, i ;

    mul( (i+1)*x-i, i=1..n) ;

    expand(%) ;

    coeff(%, x, k) ;

end proc:

MATHEMATICA

p[x_, n_] := Product[(i + 1)*x - i, {i, 1, n}];

Table[Expand[p[x, n]], {n, 0, 10}];

Table[CoefficientList[p[x, n], x], {n, 0, 10}];

Flatten[%]

CROSSREFS

Cf. A088996.

Sequence in context: A193548 A131049 A126851 * A152825 A261710 A064288

Adjacent sequences:  A142067 A142068 A142069 * A142071 A142072 A142073

KEYWORD

sign,tabl,easy

AUTHOR

Roger L. Bagula and Gary W. Adamson, Sep 15 2008

STATUS

approved

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Last modified November 12 19:19 EST 2018. Contains 317116 sequences. (Running on oeis4.)