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%I #6 Jan 15 2013 17:00:18
%S 1,1,1,1,1,1,1,-1,-1,1,1,-11,-15,-11,1,1,-51,-76,-76,-51,1,1,-204,
%T -315,-350,-315,-204,1,1,-785,-1226,-1422,-1422,-1226,-785,1,1,-2995,
%U -4683,-5523,-5775,-5523,-4683,-2995,1,1,-11431,-17830,-21142,-22528,-22528
%N Triangle t(n,m)= binomial(n+m-1,n-1) + binomial(2*n-m-1,n-1) -binomial(2*n-1,n-1) read by rows, 0<=m<=n.
%C Row sums are 1, 2, 3, 0, -35, -252, -1386, -6864, -32175, -145860, -646646,....
%F t(n,m) = t(n,n-m).
%e 1;
%e 1, 1;
%e 1, 1, 1;
%e 1, -1, -1, 1;
%e 1, -11, -15, -11, 1;
%e 1, -51, -76, -76, -51, 1;
%e 1 -204, -315, -350, -315, -204, 1;
%e 1, -785, -1226, -1422, -1422, -1226, -785, 1;
%e 1, -2995, -4683, -5523, -5775, -5523, -4683, -2995, 1;
%e 1, -11431, -17830, -21142, -22528, -22528, -21142, -17830, -11431, 1;
%e 1, -43748, -68013, -80718, -86658, -88374, -86658, -80718, -68013, -43748, 1;
%p A174952 := proc(n,m)
%p binomial(n+m-1,n-1)+binomial(2*n-m-1,n-1) -binomial(2*n-1,n-1);
%p end proc: # _R. J. Mathar_, Jan 15 2013
%Y Cf. A158498, A059481
%K sign,tabl,easy
%O 0,12
%A _Roger L. Bagula_, Apr 02 2010
%E Definition corrected and deobfuscated. _R. J. Mathar_, Jan 15 2013
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