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A176484 Triangle t(n,m) read by rows: t(n,n)= 1, t(n,m) = (-1)^(n+m)*(m+1), 0<=m<n. 1
1, -1, 1, 1, -2, 1, -1, 2, -3, 1, 1, -2, 3, -4, 1, -1, 2, -3, 4, -5, 1, 1, -2, 3, -4, 5, -6, 1, -1, 2, -3, 4, -5, 6, -7, 1, 1, -2, 3, -4, 5, -6, 7, -8, 1, -1, 2, -3, 4, -5, 6, -7, 8, -9, 1, 1, -2, 3, -4, 5, -6, 7, -8, 9, -10, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Row sums are 1, 0, 0, -1, -1, -2, -2, -3, -3, -4, -4,..

Obtained from A144328 by deleting the first column, adding a diagonal of +1's, and multiplication with (-1)^(n-m).

LINKS

Table of n, a(n) for n=0..65.

FORMULA

t(n,m) = [x^m] (x^n - sum_{j=1..n} (-1)^(j+(n mod 2)) *j*x^(j-1) ) .

EXAMPLE

1;

-1, 1;

1, -2, 1;

-1, 2, -3, 1;

1, -2, 3, -4, 1;

-1, 2, -3, 4, -5, 1;

1, -2, 3, -4, 5, -6, 1;

-1, 2, -3, 4, -5, 6, -7, 1;

1, -2, 3, -4, 5, -6, 7, -8, 1;

-1, 2, -3, 4, -5, 6, -7, 8, -9, 1;

1, -2, 3, -4, 5, -6, 7, -8, 9, -10, 1;

MATHEMATICA

p[x, 0] = 1;

p[x_, n_] := p[x, n] = x^n - Sum[(-1)^(i + Mod[n, 2])*i*x^(i - 1), {i, 1, n}];

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

Flatten[%]

CROSSREFS

Sequence in context: A318288 A088426 A124769 * A144328 A128227 A306727

Adjacent sequences:  A176481 A176482 A176483 * A176485 A176486 A176487

KEYWORD

sign,tabl,easy

AUTHOR

Roger L. Bagula, Apr 18 2010

STATUS

approved

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Last modified May 8 12:24 EDT 2021. Contains 343666 sequences. (Running on oeis4.)