A117742 Triangle read by rows: coefficient of x^n in the Taylor expansion of x/(1 - m*x - x^4) in row n, column m=1..n+2.

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

Offset

-1,8

Comments

The value in row n=-1 is set to 0 by definition.

Column m=1 is A003269, m=2 is A008999, m=3 is A052917, m=4 is A098590.

Links

Table of n, a(n) for n=-1..51.

Example

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

Mathematica

(* 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]

Crossrefs

Cf. A003269.

Sequence in context: A276380 A352724 A248723 * A117716 A211234 A359122

Adjacent sequences: A117739 A117740 A117741 * A117743 A117744 A117745

Keyword

nonn,tabl

Author

Roger L. Bagula, Apr 14 2006

Extensions

Offset set to -1 and crossrefs to columns added by Assoc. Eds. of the OEIS, Jun 15 2010

Status

approved