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.

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

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, A077899, A077925, A175722.

Sequence in context: A173934 A131504 A008311 * A337936 A296388 A081772

Adjacent sequences: A175718 A175719 A175720 * A175722 A175723 A175724

Keyword

sign,tabl

Author

Roger L. Bagula, Dec 04 2010

Status

approved