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%I #7 Jul 04 2013 17:59:55
%S 1,1,1,1,5,1,1,21,15,1,1,85,171,35,1,1,341,1795,871,70,1,1,1365,18291,
%T 19215,3321,126,1,1,5461,184275,402591,135450,10377,210,1,1,21845,
%U 1848211,8236095,5143341,716562,28017,330,1,1,87381,18503955,166570111,188253030,45270813,3069990,67617,495,1
%N Stirling-like number triangle defined by the sequence A000292=C(n+3,3).
%C Columns include A002450, A016225. The defining sequence A000292=C(n+3,3) is the sequence of partial sums of the defining sequence for number triangle A080248.
%F T(n,k) = T(n-1,k-1) + A000292(k)*T(n-1,k). Columns are generated by 1/product{k=0..n, 1-C(k+3,3)*x}.
%e Triangle begins:
%e 1;
%e 1, 1;
%e 1, 5, 1;
%e 1, 21, 15, 1;
%e 1, 85, 171, 35, 1;
%e 1, 341, 1795, 871, 70, 1;
%e 1, 1365, 18291, 19215, 3321, 126, 1;
%e 1, 5461, 184275, 402591, 135450, 10377, 210, 1;
%e For example, 171 = 21+10*15, 35 = 15+20*1.
%Y Cf. A080248, A008277.
%K easy,nonn,tabl
%O 0,5
%A _Paul Barry_, Feb 17 2003
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