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 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, 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 (list; table; graph; refs; listen; history; text; internal format)
 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 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: A003324 A110630 A129717 * A117716 A211234 A097150 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

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Last modified May 23 11:13 EDT 2013. Contains 225587 sequences.