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A117744
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Triangle read by rows: coefficient of x^n in the power series of x/(1 - m*x - x^2 + x^3 - x^5) 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, 2, 5, 10, 17, 26, 2, 11, 32, 71, 134, 227, 3, 25, 103, 297, 691, 1393, 2535, 4, 57, 332, 1243, 3564, 8549, 18052, 34647, 6, 130, 1070, 5202, 18382, 52466, 128550, 280930, 561782, 9, 297, 3449, 21771, 94809, 321989, 915417
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| -1,8
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COMMENTS
| The value in row n=-1 is set to 0 by definition.
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EXAMPLE
| 0
0, 0
1, 1, 1
1, 2, 3, 4
2, 5, 10, 17, 26
2, 11, 32, 71, 134, 227
3, 25, 103, 297, 691, 1393, 2535
4, 57, 332, 1243, 3564, 8549, 18052, 34647
6, 130, 1070, 5202, 18382, 52466, 128550, 280930, 561782
9, 297, 3449, 21771, 94809, 321989, 915417, 2277879, 5111081, 10559169
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MATHEMATICA
| (* define the polynomial*) p[x_] = p[x_] = x/(1 - m*x - x^2 + x^3 - x^5); (* 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
| Cf. A107293 (column m=1).
Sequence in context: A157000 A026346 A120636 * A091732 A109746 A061020
Adjacent sequences: A117741 A117742 A117743 * A117745 A117746 A117747
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KEYWORD
| nonn,tabl
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AUTHOR
| Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Apr 14 2006
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EXTENSIONS
| I partially edited this entry, Jun 13 2006 - N. J. A. Sloane (njas(AT)research.att.com).
Offset set to -1 by Assoc. Eds. of the OEIS, Jun 15 2010
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