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Search: id:A136531
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| A136531 |
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Coefficients of polynomial recursion with simple values: a=-b;b=1;c=1 ; B(x, n) = ((1 + a + b)*x - c)*B(x, n - 1) - a*b*B(x, n - 2). |
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+0
1
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| 1, 0, 1, 1, -1, 1, -1, 3, -2, 1, 2, -5, 6, -3, 1, -3, 10, -13, 10, -4, 1, 5, -18, 29, -26, 15, -5, 1, -8, 33, -60, 65, -45, 21, -6, 1, 13, -59, 122, -151, 125, -71, 28, -7, 1, -21, 105, -241, 338, -321, 217, -105, 36, -8, 1, 34, -185, 468, -730, 784, -609, 350, -148, 45, -9, 1
(list; table; graph; listen)
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OFFSET
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1,8
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COMMENT
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Row sums are all 1.
This recursion doesn't appear to be integration orthogonal at all.
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FORMULA
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a=-b;b=1;c=1 ; B(x, n) = ((1 + a + b)*x - c)*B(x, n - 1) - a*b*B(x, n - 2)
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EXAMPLE
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{1},
{0, 1},
{1, -1, 1},
{-1, 3, -2, 1},
{2, -5, 6, -3, 1},
{-3,10, -13, 10, -4, 1},
{5, -18, 29, -26, 15, -5, 1},
{-8,33, -60, 65, -45,21, -6, 1},
{13, -59, 122, -151, 125, -71, 28, -7, 1},
{-21, 105, -241, 338, -321, 217, -105,36, -8, 1},
{34, -185, 468, -730, 784, -609, 350, -148, 45, -9, 1}
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MATHEMATICA
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Clear[B, x, n, f, a, b, c] a = -b; c = 1; b = 1; B[x, 0] = 1; B[x, 1] = x; B[x_, n_] := B[x, n] = ((1 + a + b)*x - c)*B[x, n - 1] - a*b*B[x, n - 2]; Table[ExpandAll[B[x, n]], {n, 0, 10}]; a0 = Table[CoefficientList[B[x, n], x], {n, 0, 10}]; Flatten[a0]
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CROSSREFS
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Adjacent sequences: A136528 A136529 A136530 this_sequence A136532 A136533 A136534
Sequence in context: A136560 A105847 A048984 this_sequence A127318 A085068 A079587
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KEYWORD
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uned,tabl,sign
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Mar 23 2008
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