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A117744
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.
0
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
OFFSET
-1,8
COMMENTS
The value in row n=-1 is set to 0 by definition.
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
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]
CROSSREFS
Cf. A107293 (column m=1).
Sequence in context: A322990 A120636 A209747 * A366481 A361697 A091732
KEYWORD
nonn,tabl
AUTHOR
Roger L. Bagula, Apr 14 2006
EXTENSIONS
I partially edited this entry, Jun 13 2006 - N. J. A. Sloane.
Offset set to -1 by Assoc. Eds. of the OEIS, Jun 15 2010
STATUS
approved