cp's OEIS Frontend

A185962 Riordan array ((1-x)^2/(1-x+x^2), x(1-x)^2/(1-x+x^2)).

%I A185962 #31 Oct 18 2024 21:43:22
%S A185962 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,
%T A185962 -4,-6,-1,10,9,-7,1,-1,-4,-10,-16,-10,10,14,-8,1,0,1,0,-10,-26,-24,7,
%U A185962 20,-9,1,1,6,15,20,5,-30,-42,0,27,-10,1
%N A185962 Riordan array ((1-x)^2/(1-x+x^2), x(1-x)^2/(1-x+x^2)).
%C A185962 Riordan array (g(x),xg(x)) where g(x)=(1-x)(1-x^2)(1-x^3)/(1-x^6).
%C A185962 Inverse is A185967. Row sums are A185963.
%C A185962 Diagonal sums are A185964. Central coefficients are A185965.
%C A185962 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
%H A185962 G. C. Greubel, <a href="/A185962/b185962.txt">Table of n, a(n) for the first 50 rows, flattened</a>
%F A185962 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).
%F A185962 G.f.: 1/(1-y*x+x/(1-x)^2). - _Philippe Deléham_, Feb 07 2012
%F A185962 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
%e A185962 Triangle begins:
%e A185962    1;
%e A185962   -1,  1;
%e A185962   -1, -2,   1;
%e A185962    0, -1,  -3,   1;
%e A185962    1,  2,   0,  -4,   1;
%e A185962    1,  3,   5,   2,  -5,   1;
%e A185962    0,  0,   3,   8,   5,  -6,   1;
%e A185962   -1, -4,  -6,  -1,  10,   9,  -7,  1;
%e A185962   -1, -4, -10, -16, -10,  10,  14, -8,  1;
%e A185962    0,  1,   0, -10, -26, -24,   7, 20, -9,   1;
%e A185962    1,  6,  15,  20,   5, -30, -42,  0, 27, -10, 1;
%e A185962   ...
%e A185962 From _Philippe Deléham_, Mar 19 2012: (Start)
%e A185962 (0, -1, 2, -1/2, 1/2, 0, 0, ...) DELTA (1, 0, 0, 0, ...) begins:
%e A185962   1;
%e A185962   0,  1;
%e A185962   0, -1,  1;
%e A185962   0, -1, -2,  1;
%e A185962   0,  0, -1, -3,  1;
%e A185962   0,  1,  2,  0, -4,  1;
%e A185962   0,  1,  3,  5,  2, -5,  1;
%e A185962   ... (End)
%t A185962 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 *)
%Y A185962 Cf. A195339, A195350.
%K A185962 sign,easy,tabl
%O A185962 0,5
%A A185962 _Paul Barry_, Feb 07 2011