A136261 Triangle T(n,k) = k*A122188(n,k), read by rows.

-1, -1, 2, 1, 2, -3, -1, -2, -3, 4, 1, 2, 3, 4, -5, -1, -2, -3, -4, -5, 6, 1, 2, 3, 4, 5, 6, -7, -1, -2, -3, -4, -5, -6, -7, 8, 1, 2, 3, 4, 5, 6, 7, 8, -9, -1, -2, -3, -4, -5, -6, -7, -8, -9, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, -11

Offset

1,3

Comments

Multiplication of the columns of A122188 by their index is equivalent to differentiation of the polynomials B(n,x) defined in A122188.

Row sums are -1, 1, 0, -2, 5, -9, 14, -20, 27, -35, 44, ... =(-1)^n*A080956(n-1).

Links

Table of n, a(n) for n=1..66.

Formula

|T(n,k)| = A002260(n,k).

Example

  -1;
  -1,  2;
   1,  2, -3;
  -1, -2, -3,  4;
   1,  2,  3,  4, -5;
  -1, -2, -3, -4, -5,  6;
   1,  2,  3,  4,  5,  6, -7;
  -1, -2, -3, -4, -5, -6, -7,  8;
   1,  2,  3,  4,  5,  6,  7,  8, -9;
  -1, -2, -3, -4, -5, -6, -7, -8, -9, 10;
   1,  2,  3,  4,  5,  6,  7,  8,  9, 10, -11;

Mathematica

Clear[B, x, n] B[x, 0] = 1; B[x, 1] = -x + 1; B[x_, n_] := B[x, n] = If[n > 1, (-1)^n*(x^n - Sum[x^m, {m, 0, n - 1}])]; P[x_, n_] := D[B[x, n + 1], x]; Table[ExpandAll[P[x, n]], {n, 0, 10}]; a = Table[CoefficientList[P[x, n], x], {n, 0, 10}]; Flatten[a] Table[Apply[Plus, CoefficientList[P[x, n], x]], {n, 0, 10}];

Crossrefs

Cf. A002260, A122188.

Sequence in context: A348043 A138060 A023121 * A140756 A002260 A243732

Adjacent sequences: A136258 A136259 A136260 * A136262 A136263 A136264

Keyword

easy,tabl,sign

Author

Roger L. Bagula and Gary W. Adamson, Mar 18 2008

Status

approved