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A175721 Array T(n,m) read by antidiagonals: the coefficient of [x^m] of 1/(-x^n +1 -x^(1+n) +x +3*x^(2+n) -2*x^2 -x^(3+n)) in row n, column 1<=m. 1
0, 3, -1, -3, 4, -1, 10, -6, 3, -1, -18, 14, -4, 3, -1, 42, -24, 10, -5, 3, -1, -87, 47, -19, 12, -5, 3, -1, 190, -83, 42, -22, 11, -5, 3, -1, -405, 152, -84, 45, -20, 11, -5, 3, -1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Antidiagonal sums are: 0, 2, 0, 6, -6, 25, -50, 135, -304,...

For large n, the rows approach A077925.

LINKS

Table of n, a(n) for n=1..45.

FORMULA

G.f.: 1/( -x^n +1 -x^(1+n) +x +3*x^(2+n) -2*x^2 -x^(3+n) ).

EXAMPLE

The array starts in row n=1 with columns m>=1 as

0,3,-3,10,-18,42,-87,190,-405,873,...  A077899

-1,4,-6,14,-24,47,-83,152,-268,476,... A175722

-1,3,-4,10,-19,42,-84,174,-353,726,...

-1,3,-5,12,-22,45,-87,174,-340,670,...

-1,3,-5,11,-20,42,-83,169,-339,686,...

-1,3,-5,11,-21,44,-86,173,-343,685,...

-1,3,-5,11,-21,43,-84,170,-339,681,...

-1,3,-5,11,-21,43,-85,172,-342,685,...

-1,3,-5,11,-21,43,-85,171,-340,682,...

-1,3,-5,11,-21,43,-85,171,-341,684,...

MAPLE

A175721 := proc(m, k) 1/(-x^m + 1 - x^(1 + m) + x + 3*x^(2 + m) - 2* x^2 - x^(3 + m)) ; coeftayl(%, x=0, k) ; end proc: # R. J. Mathar, Dec 22 2010

MATHEMATICA

f[x_, m_] = ExpandAll[(x - x^(m + 1))*(1 - x - x^2) - (1 - 2*x + x^(m + 1))];

g[x_, n_] = ExpandAll[x^(m + 3)*f[1/x, m]];

a = Table[Table[SeriesCoefficient[

      Series[1/g[x, m], {x, 0, 10}], n], {n, 0, 10}], {m, 1, 10}];

Table[Table[a[[m, n - m + 1]], {m, 1, n - 1}], {n, 1, 10}]

Flatten[%]

CROSSREFS

Cf. A000045, A077925

Sequence in context: A173934 A131504 A008311 * A296388 A081772 A204217

Adjacent sequences:  A175718 A175719 A175720 * A175722 A175723 A175724

KEYWORD

sign,tabl

AUTHOR

Roger L. Bagula, Dec 04 2010

STATUS

approved

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Last modified February 25 16:14 EST 2018. Contains 299653 sequences. (Running on oeis4.)