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Search: id:A156960
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| A156960 |
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q-Carlitz-Al-Salam-Appell polynomial coefficients:q=2; p(x,n)=x*p[x, n - 1] - (1 - q^(n - 1))*q^(n - 2)*p[x, n - 2]. |
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+0
1
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| 1, 0, 1, 1, 0, 1, 0, 7, 0, 1, 28, 0, 35, 0, 1, 0, 868, 0, 155, 0, 1, 13888, 0, 18228, 0, 651, 0, 1, 0, 1763776, 0, 330708, 0, 2667, 0, 1, 112881664, 0, 149920960, 0, 5622036, 0, 10795, 0, 1, 0, 57682530304, 0, 10944230080, 0, 92672916, 0, 43435, 0, 1
(list; table; graph; listen)
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OFFSET
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0,8
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COMMENT
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Row sums are:
{1, 1, 2, 8, 64, 1024, 32768, 2097152, 268435456, 68719476736, 35184372088832,...}.
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REFERENCES
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T Ernst,The different tongues of q - calculus,Proceedings of the Estonian Academy of Sciences, 2008 - kirj.ee, 2-81-99,pp.14-15
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FORMULA
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q=2; p(x,n)=x*p[x, n - 1] - (1 - q^(n - 1))*q^(n - 2)*p[x, n - 2];
t(n,m)=coefficients(p(x,n)).
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EXAMPLE
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{1},
{0, 1},
{1, 0, 1},
{0, 7, 0, 1},
{28, 0, 35, 0, 1},
{0, 868, 0, 155, 0, 1},
{13888, 0, 18228, 0, 651, 0, 1},
{0, 1763776, 0, 330708, 0, 2667, 0, 1},
{112881664, 0, 149920960, 0, 5622036, 0, 10795, 0, 1},
{0, 57682530304, 0, 10944230080, 0, 92672916, 0, 43435, 0, 1},
{14766727757824, 0, 19669742833664, 0, 746396491456, 0, 1504831636, 0, 174251, 0, 1}
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MATHEMATICA
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Clear[p, x, n, q];
p[x, 0] := 1; p[x, 1] := x;
p[x_, n_] := p[x, n] = x*p[x, n - 1] - (1 - q^(n - 1))*q^(n - 2)*p[x, n - 2];
q = 2; Table[ExpandAll[p[x, n]], {n, 0, 10}];
Table[CoefficientList[ExpandAll[p[x, n]], x], {n, 0, 10}];
Flatten[%]
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CROSSREFS
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Sequence in context: A121570 A153626 A101031 this_sequence A067840 A118858 A118288
Adjacent sequences: A156957 A156958 A156959 this_sequence A156961 A156962 A156963
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KEYWORD
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nonn,tabl,uned
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Feb 19 2009
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