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A136255 Triangle T(n,k) read by rows: T(n,k) = (k+1) * A137276(n,k+1).

%I A136255 #10 May 15 2016 16:50:44
%S A136255 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,
%T A136255 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,
%U A136255 -75,0,35,0,84,0,-63,0,11
%N A136255 Triangle T(n,k) read by rows: T(n,k) = (k+1) * A137276(n,k+1).
%C A136255 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.
%F A136255 T(n,k) = (k+1) * A137276(n,k+1) .
%e A136255 Triangle starts:
%e A136255 {1},
%e A136255 {0, 2},
%e A136255 {1, 0, 3},
%e A136255 {0, 0, 0, 4},
%e A136255 {-3, 0, -3, 0, 5},
%e A136255 {0, -6, 0, -8, 0, 6},
%e A136255 {5, 0, -6, 0, -15, 0, 7},
%e A136255 {0, 16, 0, 0, 0, -24, 0, 8},
%e A136255 {-7, 0, 30, 0, 15, 0, -35, 0, 9},
%e A136255 {0, -30, 0, 40, 0,42, 0, -48, 0, 10},
%e A136255 {9, 0, -75, 0, 35, 0, 84, 0, -63, 0, 11},
%e A136255 ...
%p A136255 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:
%p A136255 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) ;
%t A136255 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}]
%Y A136255 Cf. A138034, A135929, A135936, A137276, A137277, A137289.
%K A136255 tabl,sign
%O A136255 1,3
%A A136255 _Roger L. Bagula_, Mar 17 2008
%E A136255 Edited by the Associate Editors of the OEIS, Aug 27 2009
%E A136255 Edited by and new name from _Joerg Arndt_, May 15 2016