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A139144
Irregular triangle read by rows: let c = -(x - x^2), b = (-1 - a + 2 x)/x, and a = 0, expansion of p(x, n) = (a + b*x)*p(x, n - 1) + c*p(x, n - 2).
0
1, 0, 0, 1, -1, 0, 1, -3, 2, 0, 1, -4, 6, -3, 0, 1, -5, 10, -10, 4, 0, -1, 6, -15, 20, -15, 5, 0, 1, -9, 33, -65, 75, -49, 14, 0, -1, 12, -58, 152, -240, 234, -132, 33, 0, 1, -15, 92, -310, 642, -854, 724, -360, 80, 0, -1, 18, -135, 564, -1472, 2530, -2906, 2174, -965, 193
OFFSET
1,8
EXAMPLE
{1},
{0},
{0, 1, -1},
{0, 1, -3, 2},
{0, 1, -4, 6, -3},
{0, 1, -5, 10, -10, 4},
{0, -1,6, -15, 20, -15, 5},
{0, 1, -9, 33, -65, 75, -49, 14},
{0, -1, 12, -58, 152, -240, 234, -132, 33},
{0, 1, -15, 92, -310, 642, -854, 724, -360, 80},
{0, -1, 18, -135, 564, -1472, 2530, -2906, 2174, -965, 193}
MATHEMATICA
p[x, 0] = 1; p[x, 1] = 0; p[x, 2] = -x^2 + x; p[x, 3] = 2*x^3 - 3*x^2 + x; p[x, 4] = -3*x^4 + 6*x^3 - 4*x^2 + x; p[x, 5] = 4*x^5 - 10*x^4 + 10*x^3 - 5*x^2 + x;
c = -(x - x^2); b = (-1 - a + 2 x)/x; a = 0;
p[x_, n_] := p[x, n] = (a + b*x)*p[x, n - 1] + c*p[x, n - 2];
Table[ExpandAll[p[x, n]], {n, 0, 10}];
a0 = Table[CoefficientList[p[x, n], x], {n, 0, 10}];
Flatten[a0]
Table[Apply[Plus, CoefficientList[p[x, n], x]], {n, 0, 10}]
CROSSREFS
Sequence in context: A329278 A348966 A008783 * A360866 A373451 A081576
KEYWORD
uned,tabf,sign
AUTHOR
Roger L. Bagula, Jun 05 2008
STATUS
approved