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Search: id:A133135
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| A133135 |
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Third column of the inverse of the triangle of polynomial coefficients P(0,x)=1, 2P(n,x)=(1+x)*[(1+x)^(n-1)+x^(n-1)]. |
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+0
6
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| 1, -2, 2, -1, 1, -4, 4, 13, -13, -142, 142, 1931, -1931, -36296, 36296, 893273, -893273, -27927346, 27927346, 1081725559, -1081725559, -50861556172, 50861556172, 2854289486309, -2854289486309, -188475382997654, 188475382997654, 14467150771771043, -14467150771771043
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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The triangle with [x^k] P(n,x) starts
1;
1, 1;
1/2, 3/2, 1;
1/2, 3/2, 2, 1;
1/2, 2, 3, 5/2, 1;
1/2, 5/2, 5, 5, 3, 1;
1/2, 3,15/2, 10,15/2, 7/2, 1;
1/2, 7/2,21/2,35/2,35/2,21/2, 4, 1;
1/2, 4, 14, 28, 35, 28, 14, 9/2, 1;
1/2, 9/2, 18, 42, 63, 63, 42, 18, 5, 1;
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EXAMPLE
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The inverse of the triangle of coefficients starts
1;
-1, 1;
1, -3/2, 1;
-1, 3/2, -2, 1;
1, -5/4, 2, -5/2, 1;
-1, 5/4 -1, 5/2, -3, 1;
1, -7/4, 1, 0, 3, -7/2, 1;
-1, 7/4,-4, 0, 2, 7/2,-4, 1;
1, 3/8, 4,-21/2, -2, 21/4, 4,-9/2, 1;
-1, -3/8,13, 21/2,-26,-21/4,10, 9/2,-5, 1;
and defines the sequence in its third column.
Apart from the numbers along the diagonal, the absolute values show up in pairs if read along columns. Conjectures: Starting with the third line, columns are alternatingly fractions and integers. The row sums (1, 0, 1/2, -1/2, 1/4, -1/4, 3/4, -3/4, -11/8, 11/8,..) also show up in pairs from the third row on.
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CROSSREFS
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Sequence in context: A053390 A140643 A108017 this_sequence A132311 A121697 A124976
Adjacent sequences: A133132 A133133 A133134 this_sequence A133136 A133137 A133138
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KEYWORD
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sign
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AUTHOR
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Paul Curtz (bpcrtz(AT)free.fr), Sep 21 2007
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EXTENSIONS
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Edited and extended by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Aug 02 2008
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