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Search: id:A110162
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| A110162 |
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Riordan array ((1-x)/(1+x),x/(1+x)^2). |
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+0
9
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| 1, -2, 1, 2, -4, 1, -2, 9, -6, 1, 2, -16, 20, -8, 1, -2, 25, -50, 35, -10, 1, 2, -36, 105, -112, 54, -12, 1, -2, 49, -196, 294, -210, 77, -14, 1, 2, -64, 336, -672, 660, -352, 104, -16, 1, -2, 81, -540, 1386, -1782, 1287, -546, 135, -18, 1, 2, -100, 825, -2640, 4290, -4004, 2275, -800, 170, -20, 1
(list; table; graph; listen)
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OFFSET
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0,2
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COMMENT
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Inverse of Riordan array A094527. Rows sums are A099837. Diagonal sums are A110164. Product of Riordan array A102587 and inverse binomial transform (1/(1+x),x/(1+x)).
Coefficients of polynomials related to Cartan matrices of types C_n and B_n: p(x, n) = (-2 + x)*p(x, n - 1) - p(x, n - 2), with p(x,0) = 1; p(x,1) = 2-x; p(x,2) = x^2-4*x-2. - Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Apr 12 2008
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FORMULA
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T(n,k)=C(n+k,n-k)(-1)^(n-k)-C(n+k-1,n-k-1)(-1)^(n-k-1); - Paul Barry (pbarry(AT)wit.ie), Mar 22 2007
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EXAMPLE
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Rows begin
1;
-2,1;
2,-4,1;
-2,9,-6,1;
2,-16,20,-8,1;
-2,25,-50,35,-10,1;
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CROSSREFS
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Cf. A128411. See A127677 for an almost identical triangle.
Cf. A136674, A053122.
Adjacent sequences: A110159 A110160 A110161 this_sequence A110163 A110164 A110165
Sequence in context: A113413 A125694 A136678 this_sequence A087704 A119765 A077901
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KEYWORD
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easy,sign,tabl
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AUTHOR
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Paul Barry (pbarry(AT)wit.ie), Jul 14 2005
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