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A136255
Triangle T(n,k) read by rows: T(n,k) = (k+1) * A137276(n,k+1).
1
1, 0, 2, 1, 0, 3, 0, 0, 0, 4, -3, 0, -3, 0, 5, 0, -6, 0, -8, 0, 6, 5, 0, -6, 0, -15, 0, 7, 0, 16, 0, 0, 0, -24, 0, 8, -7, 0, 30, 0, 15, 0, -35, 0, 9, 0, -30, 0, 40, 0, 42, 0, -48, 0, 10, 9, 0, -75, 0, 35, 0, 84, 0, -63, 0, 11
OFFSET
1,3
COMMENTS
Row sums are 1, 2, 4, 4, -1, -8, -9, 0, 12, 14, 1, ... with g.f. x*(1+3*x^2) / (x^2-x+1)^2.
FORMULA
T(n,k) = (k+1) * A137276(n,k+1) .
EXAMPLE
Triangle starts:
{1},
{0, 2},
{1, 0, 3},
{0, 0, 0, 4},
{-3, 0, -3, 0, 5},
{0, -6, 0, -8, 0, 6},
{5, 0, -6, 0, -15, 0, 7},
{0, 16, 0, 0, 0, -24, 0, 8},
{-7, 0, 30, 0, 15, 0, -35, 0, 9},
{0, -30, 0, 40, 0,42, 0, -48, 0, 10},
{9, 0, -75, 0, 35, 0, 84, 0, -63, 0, 11},
...
MAPLE
B := proc(n, x) if n = 0 then 1; else add( (-1)^j*binomial(n-j, j)*(n-4*j)/(n-j)*x^(n-2*j), j=0..n/2) ; fi; end:
A136255 := proc(n, k) diff( B(n, x), x) ; coeftayl(%, x=0, k) ; end: seq( seq(A136255(n, k), k=0..n-1), n=1..15) ;
MATHEMATICA
B[x, 0] = 1; B[x, 1] = x; B[x, 2] = 2 + x^2; B[x, 3] = x + x^3; B[x, 4] = -2 + x^4; B[x_, n_] := B[x, n] = x*B[x, n-1] - B[x, n-2]; P[x_, n_] := D[B[x, n + 1], x]; Flatten @ Table[CoefficientList[P[x, n], x], {n, 0, 10}]
CROSSREFS
KEYWORD
tabl,sign
AUTHOR
Roger L. Bagula, Mar 17 2008
EXTENSIONS
Edited by the Associate Editors of the OEIS, Aug 27 2009
Edited by and new name from Joerg Arndt, May 15 2016
STATUS
approved