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A202480 Riordan array (1/(1-x), x(2x-1)/(1-x)^2).

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%I A202480 #8 Jun 02 2025 07:25:08
%S A202480 1,1,-1,1,-1,1,1,0,1,-1,1,2,-1,-1,1,1,5,-5,2,1,-1,1,9,-10,8,-3,-1,1,1,
%T A202480 14,-14,14,-11,4,1,-1,1,20,-14,14,-17,14,-5,-1,1,1,27,-6,0,-9,19,-17,
%U A202480 6,1,-1
%N A202480 Riordan array (1/(1-x), x(2x-1)/(1-x)^2).
%C A202480 Row sums are Fibonacci(n-1) = A000045(n-1).
%C A202480 Diagonal sums are A078003(n).
%C A202480 (Sum_{j, 0<=j<=k} T(k,j))/(1-2x)^k gives g.f. of column A165241(n+k-1,k-1) in triangular array in A165241.
%F A202480 T(n,k) = 2*T(n-1,k) + 2*T(n-2,k-1) - T(n-1,k-1) - T(n-2,k).
%F A202480 T(n,k) = (-1)^n*A124341(n,k).
%e A202480 Triangle begins :
%e A202480 1
%e A202480 1, -1
%e A202480 1, -1, 1
%e A202480 1, 0, 1, -1
%e A202480 1, 2, -1, -1, 1
%e A202480 1, 5, -5, 2, 1, -1
%e A202480 1, 9, -10, 8, -3, -1, 1
%e A202480 1, 14, -14, 14, -11, 4, 1, -1
%e A202480 (1+x^2-x^3)/(1-2x)^3 is the g.f of column A165241(n+2,2) := 1, 6, 25, 85, 258, 728, 1952, 5040, ...
%Y A202480 Cf. A000012, A080956, A000045, A078003, A124341, A165241
%K A202480 easy,sign,tabl
%O A202480 0,12
%A A202480 _Philippe Deléham_, Dec 20 2011