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Search: id:A109954
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| A109954 |
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Riordan array (1/(1+x)^3,x/(1+x)^2). |
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+0
5
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| 1, -3, 1, 6, -5, 1, -10, 15, -7, 1, 15, -35, 28, -9, 1, -21, 70, -84, 45, -11, 1, 28, -126, 210, -165, 66, -13, 1, -36, 210, -462, 495, -286, 91, -15, 1, 45, -330, 924, -1287, 1001, -455, 120, -17, 1, -55, 495, -1716, 3003, -3003, 1820, -680, 153, -19, 1, 66, -715, 3003, -6435, 8008, -6188, 3060, -969, 190, -21, 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 (c(x)^3,xc(x)^2)) or A050155, with c(x) the g.f. of A000108. Unsigned array is the Riordan array (1/(1-x)^3,x(1-x)^2), with T(n,k)=binomial(n+k+2,2k+2)
Triangle of coefficients of polynomials defined by: c0=1; p(x, n) = (2 + c0 - x)*p(x, n - 1) + (-1 - c0 (2 - x))*p(x, n - 2) + c0*p(x, n - 3). Setting c0=0 gives A136674. - Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Apr 08 2008
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FORMULA
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Number triangle T(n, k)=(-1)^(n+k)*binomial(n+k+2, 2k+2) [offset (0, 0)].
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EXAMPLE
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Rows begin
1;
-3,1;
6,-5,1;
-10,15,-7,1;
15,-35,28,-9,1;
-21,70,-84,45,-11,1;
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MATHEMATICA
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c0 = 1; p[x, -1] = 0; p[x, 0] = 1; p[x, 1] = 2 - x + c0; p[x_, n_] := p[x, n] = (2 + c0 - x)*p[x, n - 1] + (-1 - c0 (2 - x))*p[x, n - 2] + c0*p[x, n - 3]; Table[ExpandAll[p[x, n]], {n, 0, 10}]; a = Table[CoefficientList[p[x, n], x], {n, 0, 10}]; Flatten[a] - Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Apr 08 2008
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CROSSREFS
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Sequence in context: A061702 A112351 A143858 this_sequence A153641 A133545 A153091
Adjacent sequences: A109951 A109952 A109953 this_sequence A109955 A109956 A109957
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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 06 2005
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