OFFSET
0,5
COMMENTS
Riordan array (g(x),xg(x)) where g(x)=(1-x)(1-x^2)(1-x^3)/(1-x^6).
Subtriangle of the triangle given by (0, -1, 2, -1/2, 1/2, 0, 0, 0, 0, 0, 0, 0, ...) DELTA (1, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938. - Philippe Deléham, Mar 19 2012
LINKS
G. C. Greubel, Table of n, a(n) for the first 50 rows, flattened
FORMULA
T(n,k) = Sum_{i=0..(2*k+2)} C(2*k+2,i)*Sum_{j=0..(n-k-i)} C(k+j,j)*C(j,n-k-i-j)*(-1)^(n-k-j).
G.f.: 1/(1-y*x+x/(1-x)^2). - Philippe Deléham, Feb 07 2012
T(n,k) = T(n-1,k) + T(n-1,k-1) - T(n-2,k) - 2*T(n-2,k-1) + T(n-3,k-1), T(0,0) = T(1,1) = T(2,2) = 1, T(1,0) = T(2,0) = -1, T(2,1) = -2, T(n,k) = 0 if k<0 or if k>n. - Philippe Deléham , Nov 11 2013
EXAMPLE
Triangle begins:
1;
-1, 1;
-1, -2, 1;
0, -1, -3, 1;
1, 2, 0, -4, 1;
1, 3, 5, 2, -5, 1;
0, 0, 3, 8, 5, -6, 1;
-1, -4, -6, -1, 10, 9, -7, 1;
-1, -4, -10, -16, -10, 10, 14, -8, 1;
0, 1, 0, -10, -26, -24, 7, 20, -9, 1;
1, 6, 15, 20, 5, -30, -42, 0, 27, -10, 1;
...
From Philippe Deléham, Mar 19 2012: (Start)
(0, -1, 2, -1/2, 1/2, 0, 0, ...) DELTA (1, 0, 0, 0, ...) begins:
1;
0, 1;
0, -1, 1;
0, -1, -2, 1;
0, 0, -1, -3, 1;
0, 1, 2, 0, -4, 1;
0, 1, 3, 5, 2, -5, 1;
... (End)
MATHEMATICA
CoefficientList[CoefficientList[Series[1/(1 - y*x + x/(1 - x)^2), {x, 0, 10}, {y, 0, 10}], x], y] // Flatten (* G. C. Greubel, Jul 23 2017 *)
CROSSREFS
KEYWORD
AUTHOR
Paul Barry, Feb 07 2011
STATUS
approved