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Search: id:A155994
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| A155994 |
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A triangle of polynomial coefficients: p(x,n)=-(ChebyshevU[n, x] - ((x + 1)^n - (1 - x)^n)); sp(x,n) = p(x, n) + x^n*p(1/x, n). |
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+0
1
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| -2, -3, 8, -3, -6, 10, 10, -6, -17, 16, 24, 16, -17, -30, 4, 52, 52, 4, -30, -63, 24, 56, 80, 56, 24, -63, -126, 22, 234, -10, -10, 234, 22, -126, -257, 32, 488, 224, -480, 224, 488, 32, -257, -510, 8, 1096, 328, -420, -420, 328, 1096, 8, -510, -1023, 40, 2244, 480
(list; table; graph; listen)
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OFFSET
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0,1
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COMMENT
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Row sums are:
{-2, 0, 2, 8, 22, 52, 114, 240, 494, 1004, 2026,...}.
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FORMULA
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p(x,n)=-(ChebyshevU[n, x] - ((x + 1)^n - (1 - x)^n));
sp(x,n) = p(x, n) + x^n*p(1/x, n).
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EXAMPLE
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{-2},
{},
{-3, 8, -3},
{-6, 10, 10, -6},
{-17, 16, 24, 16, -17},
{-30, 4, 52, 52, 4, -30},
{-63, 24, 56, 80, 56, 24, -63},
{-126, 22, 234, -10, -10, 234, 22, -126},
{-257, 32, 488, 224, -480, 224, 488, 32, -257},
{-510, 8, 1096, 328, -420, -420, 328, 1096, 8, -510},
{-1023, 40, 2244, 480, -1232, 1008, -1232, 480, 2244, 40, -1023}
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MATHEMATICA
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p[x_, n_] =-(ChebyshevU[n, x] - ((x + 1)^n - (1 - x)^n));
sp[x_, n_] = p[x, n] + x^n*p[1/x, n];
Table[FullSimplify[ExpandAll[sp[x, n]]], {n, 0, 10}];
Table[CoefficientList[FullSimplify[ExpandAll[sp[x, n]]], x], {n, 0, 10}]; Q Flatten[%]
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CROSSREFS
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Sequence in context: A058485 A011326 A154826 this_sequence A011162 A079555 A100870
Adjacent sequences: A155991 A155992 A155993 this_sequence A155995 A155996 A155997
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KEYWORD
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sign,tabl,uned
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Feb 01 2009
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