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Search: id:A117716
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| A117716 |
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Triangle read by rows: based on expansion A000930 :x/(1-m*x-x3)=Sum[A000930[n,m]*x^n/n!,{n,0,Infinity}]. |
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2
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| 0, 0, 0, 1, 1, 1, 1, 2, 3, 4, 1, 4, 9, 16, 25, 2, 9, 28, 65, 126, 217, 3, 20, 87, 264, 635, 1308, 2415, 4, 44, 270, 1072, 3200, 7884, 16954, 32960, 6, 97, 838, 4353, 16126, 47521, 119022, 264193, 534358, 9, 214, 2601, 17676, 81265, 286434, 835569, 2117656
(list; table; graph; listen)
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OFFSET
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0,8
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REFERENCES
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Steven Wolfram, The Mathematica Book,Cambridge University Press, 3rd ed. 1996, page 728
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FORMULA
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a(n,m) = A000930[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
2, 9, 28, 65, 126, 217
3, 20, 87, 264, 635, 1308, 2415
4, 44, 270, 1072, 3200, 7884, 16954, 32960
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MATHEMATICA
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(* define the polynomial*) p[x_] = x/(1 - m*x - x3); (* 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. A000930, A117715.
Sequence in context: A110630 A129717 A117742 this_sequence A097150 A087165 A083480
Adjacent sequences: A117713 A117714 A117715 this_sequence A117717 A117718 A117719
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KEYWORD
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nonn,tabl,uned
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Apr 13 2006, corrected Apr 15 2006
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