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A117742
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Triangle read by rows: coefficient of x^n in the Taylor expansion of x/(1 - m*x - x^4) in row n, column m=1..n+2.
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0
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0, 0, 0, 1, 1, 1, 1, 2, 3, 4, 1, 4, 9, 16, 25, 1, 8, 27, 64, 125, 216, 2, 17, 82, 257, 626, 1297, 2402, 3, 36, 249, 1032, 3135, 7788, 16821, 32784, 4, 76, 756, 4144, 15700, 46764, 117796, 262336, 531684, 5, 160, 2295, 16640, 78625, 280800, 824915, 2099200
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OFFSET
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-1,8
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COMMENTS
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The value in row n=-1 is set to 0 by definition.
Column m=1 is A003269, m=2 is A008999, m=3 is A052917, m=4 is A098590.
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LINKS
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Table of n, a(n) for n=-1..51.
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EXAMPLE
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0
0, 0
1, 1, 1
1, 2, 3, 4
1, 4, 9, 16, 25
1, 8, 27, 64, 125, 216
2, 17, 82, 257, 626, 1297, 2402
3, 36, 249, 1032, 3135, 7788, 16821, 32784
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MATHEMATICA
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(* define the polynomial*) p[x_] = x/(1 - m*x - x^4); (* Taylor derivative expansion of the polynomial*) a = Table[Flatten[{{p[0]}, Table[Coefficient[Series[p[x], {x, 0, 30}], x^n], {n, 1, 10}]}], {m, 1, 10}] (*antidiagonal expansion to give triangular function*) b = Join[{{ 0}}, Delete[Table[Table[a[[n]][[m]], {n, 1, m + 1}], {m, 0, 9}], 1]] Flatten[b]
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CROSSREFS
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Cf. A003269.
Sequence in context: A003324 A110630 A129717 * A117716 A211234 A097150
Adjacent sequences: A117739 A117740 A117741 * A117743 A117744 A117745
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KEYWORD
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nonn,tabl
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AUTHOR
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Roger L. Bagula, Apr 14 2006
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EXTENSIONS
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Offset set to -1 and crossrefs to columns added by Assoc. Eds. of the OEIS, Jun 15 2010
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STATUS
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approved
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