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%I #6 Aug 12 2015 02:19:14
%S 1,0,1,0,0,1,0,0,1,1,0,0,0,1,1,0,0,0,0,2,1,0,0,0,0,1,2,1,0,0,0,0,0,1,
%T 3,1,0,0,0,0,0,0,3,3,1,0,0,0,0,0,0,1,3,4,1,0,0,0,0,0,0,0,1,6,4,1,0,0,
%U 0,0,0,0,0,0,4,6,5,1,0,0,0,0,0,0,0,0,1,4,10,5,1,0,0,0,0,0,0,0,0,0,1,10,10,6
%N Triangle read by rows: expansion of (1+x*y)/(1-x^2*y^2-x^3*y^2).
%C Row sums give A000931(n+5). Diagonal sums are A124789.
%F Number triangle T(n,k) = binomial(floor(k/2),n-k).
%F Column k has g.f. x^k*(1+x)^floor(k/2). - _Paul Barry_, Feb 01 2007
%e Triangle begins
%e 1,
%e 0, 1,
%e 0, 0, 1,
%e 0, 0, 1, 1,
%e 0, 0, 0, 1, 1,
%e 0, 0, 0, 0, 2, 1,
%e 0, 0, 0, 0, 1, 2, 1,
%e 0, 0, 0, 0, 0, 1, 3, 1,
%e 0, 0, 0, 0, 0, 0, 3, 3, 1,
%e 0, 0, 0, 0, 0, 0, 1, 3, 4, 1,
%e 0, 0, 0, 0, 0, 0, 0, 1, 6, 4, 1
%p A124788 := proc(n,k) binomial(floor(k/2),n-k) ; end: for n from 0 to 20 do for k from 0 to n do printf("%d, ",A124788(n,k)) ; od ; od ; # _R. J. Mathar_, Feb 10 2007
%Y Cf. A124745.
%K easy,nonn,tabl
%O 0,20
%A _Paul Barry_, Nov 07 2006
%E More terms from _R. J. Mathar_, Feb 10 2007
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