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Search: id:A117742
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| A117742 |
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Triangular expansion of A003269 using the rational polynomial:p[x_] = x/(1 - m*x - x^4);. |
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+0
1
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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
(list; graph; listen)
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OFFSET
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0,8
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FORMULA
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a(n,m)= A003296[n,m]
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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 this_sequence A117716 A097150 A087165
Adjacent sequences: A117739 A117740 A117741 this_sequence A117743 A117744 A117745
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KEYWORD
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nonn,uned,probation
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Apr 14 2006
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