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%I #3 Mar 30 2012 16:49:03
%S 1,0,1,0,2,1,0,5,6,2,0,15,29,20,5,0,55,148,158,80,16,0,239,818,1185,
%T 910,366,61,0,1199,4964,9094,9392,5696,1904,272,0,6810,32989,73026,
%U 94833,77011,38719,11080,1385,0,43108,238931,619904,970152,988040,663904,285424,71424,7936
%N Triangle T(n,k), 0<=k<=n, formed from coefficients when formula for n-th diagonal of triangle in A059718 is written as a sum of binomial coefficients.
%C I would very much like to find a formula for this - _N. J. A. Sloane_.
%e 1; 0,1; 0,2,1; 0,5,6,2; 0,15,29,20,5; ... E.g. the n=3 diagonal in A059718 has the formula b(m) = 0 + 5*m + 6*C(m,2) + 2*C(m,3) and so the third row here is 0, 5, 6, 2.
%Y Interesting because it connects a mysterious sequence (A059219, the left edge) with a known sequence (A000111, the right edge). Cf. A059724, A059725, A059726.
%K nonn,tabl,nice
%O 0,5
%A _N. J. A. Sloane_, Feb 09 2001
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