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Search: id:A103423
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| A103423 |
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Polynomials interpolating their own integral coefficients, read by row. The leading coefficients are positive and minimal. |
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+0
3
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| 1, 1, 0, 1, -1, -1, 10, -29, -6, 19, 57, -325, 287, 423, -19, 12813, -120862, 291323, 44088, -355855, -227362, 1286795, -18146731, 79841909, -85635661, -123338281, 64989065, 145991969, 13131073916, -258931801371, 1776194531596, -4499161007143, 489428412300, 8437850634901
(list; table; graph; listen)
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OFFSET
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0,7
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FORMULA
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a(n, k)=sum{i=0, n}a(n, i)*k^i, 0<=k<=n.
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EXAMPLE
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1; x; x^2-x-1; 10*x^3-29*x^2-6*x+19; 57*x^4-325*x^3+287*x^2+423*x-19;
12813*x^5-120862*x^4+291323*x^3+44088*x^2-355855*x-227362.
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PROGRAM
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(PARI) { f(n) = local(v); v=matkerint(matrix(n+1, n+1, i, j, (i-1)^(j-1)-(i==j))); c=vector(n+1, i, v[n+2-i, 1]); if(c[1]<0, for(i=1, n+1, c[i]=-c[i])); return(c); } \ function f(n) generate coefficients of the polynomial of degree n (Alekseyev)
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CROSSREFS
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Cf. A103417, A103418.
Adjacent sequences: A103420 A103421 A103422 this_sequence A103424 A103425 A103426
Sequence in context: A116973 A003665 A066527 this_sequence A102542 A098751 A009771
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KEYWORD
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sign,tabl
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AUTHOR
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Nikolaus Meyberg (Nikolaus.Meyberg(AT)t-online.de), Feb 05 2005
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EXTENSIONS
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More terms from Max Alekseyev (maxal(AT)cs.ucsd.edu), Feb 09 2005
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