%I A115524
%S A115524 1,1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0,0,0,1,1,0,0,1,0,0,0,1,0,0,0,0,0,0,1,
1,0,0,0,
%T A115524 1,0,0,0,0,1,0,0,0,0,0,0,0,0,1,1,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,0,0,0,
0,0,1,1,0,0,
%U A115524 0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,1,0,0,0,
0,0,0,0,1,0
%V A115524 1,1,-1,-1,0,1,0,0,1,-1,0,-1,0,0,1,0,0,0,0,1,-1,0,0,-1,0,0,0,1,0,0,0,0,
0,0,1,-1,0,0,0,
%W A115524 -1,0,0,0,0,1,0,0,0,0,0,0,0,0,1,-1,0,0,0,0,-1,0,0,0,0,0,1,0,0,0,0,0,0,
0,0,0,0,1,-1,0,0,
%X A115524 0,0,0,-1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,-1,0,0,0,0,0,0,-1,0,
0,0,0,0,0,0,1,0
%N A115524 Number triangle (1,-x)+(x,x)/2+(x,-x)/2-(x^2,x^2) (expressed using the
notation of stretched Riordan arrays).
%C A115524 Row sums are A000007. Diagonal sums are A115525. Matrix inverse is A115526.
Row sums of inverse are A023416(n+2).
%F A115524 Column k has g.f. (-x)^k+(x(-x)^k+x^(k+1))/2-x^(2k+2); Number triangle
T(n, k)=(-1)^n*(if(n=k, 1, 0) OR if(n=2k+2, -1, 0) OR if(n=k+1, -(1+(-1)^k)/
2, 0)).
%F A115524 G.f.: (1+x-x*y)/(1-x^2*y^2)-x^2/(1-x^2*y); - Paul Barry (pbarry(AT)wit.ie),
Feb 02 2006
%e A115524 Triangle begins
%e A115524 1,
%e A115524 1, -1,
%e A115524 -1, 0, 1,
%e A115524 0, 0, 1, -1,
%e A115524 0, -1, 0, 0, 1,
%e A115524 0, 0, 0, 0, 1, -1,
%e A115524 0, 0, -1, 0, 0, 0, 1,
%e A115524 0, 0, 0, 0, 0, 0, 1, -1,
%e A115524 0, 0, 0, -1, 0, 0, 0, 0, 1,
%e A115524 0, 0, 0, 0, 0, 0, 0, 0, 1, -1,
%e A115524 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 1,
%e A115524 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1,
%e A115524 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 1,
%e A115524 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1,
%Y A115524 Sequence in context: A010056 A155898 A115952 this_sequence A117198 A054525
A065333
%Y A115524 Adjacent sequences: A115521 A115522 A115523 this_sequence A115525 A115526
A115527
%K A115524 easy,sign,tabl
%O A115524 0,1
%A A115524 Paul Barry (pbarry(AT)wit.ie), Jan 25 2006
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