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 A117724 Triangle with the coefficient [x^n] x/(1-m*x^2-x^3) in row n, columns m = 1..n+2. 2
 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 2, 3, 4, 5, 1, 1, 1, 1, 1, 1, 1, 4, 9, 16, 25, 36, 49, 2, 4, 6, 8, 10, 12, 14, 16, 2, 9, 28, 65, 126, 217, 344, 513, 730, 3, 12, 27, 48, 75, 108, 147, 192, 243, 300, 4, 22, 90, 268, 640, 1314, 2422, 4120, 6588, 10030, 14674, 5, 33 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET -1,12 COMMENTS The column m=1 is A000931. m=2 is essentially A008346, m=3 essentially A052931. Row n=-1 contains a single 0 by convention. LINKS Nathaniel Johnston, Table of n, a(n) for n = -1..5000 EXAMPLE The table starts: 0; 0, 0; 1, 1, 1; 0, 0, 0, 0; 1, 2, 3, 4, 5; 1, 1, 1, 1, 1, 1; 1, 4, 9, 16, 25, 36, 49; 2, 4, 6, 8, 10, 12, 14, 16; 2, 9, 28, 65, 126, 217, 344, 513, 730; 3, 12, 27, 48, 75, 108, 147, 192, 243, 300; MAPLE t:=taylor(x/(1-m*x^2-x^3), x, 11):seq(seq(coeff(t, x, n), m=1..n+2), n=-1..10); # Nathaniel Johnston, Apr 27 2011 MATHEMATICA (* define the polynomial *) p[x_] = x/(1 - m*x^2 - x^3); (* 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]] CROSSREFS Cf. A000931. Sequence in context: A256306 A030548 A346690 * A255826 A339256 A277544 Adjacent sequences: A117721 A117722 A117723 * A117725 A117726 A117727 KEYWORD nonn,tabl,easy AUTHOR Roger L. Bagula, Apr 13 2006 EXTENSIONS Sign in definition corrected, offset set to -1 by Assoc. Eds. of the OEIS, Jun 15 2010 STATUS approved

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Last modified December 6 18:39 EST 2022. Contains 358644 sequences. (Running on oeis4.)