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, 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.

Links

Table of n, a(n) for n=-1..50.

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

Adjacent sequences: A117741 A117742 A117743 * A117745 A117746 A117747

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