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A136261 Triangle T(n,k) = k*A122188(n,k), read by rows. 0
-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 (list; table; graph; refs; listen; history; text; internal format)
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
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
Sequence in context: A348043 A138060 A023121 * A140756 A002260 A243732
KEYWORD
easy,tabl,sign
AUTHOR
STATUS
approved

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Last modified March 28 14:37 EDT 2024. Contains 371254 sequences. (Running on oeis4.)