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%I A080249 #7 Jul 04 2013 17:59:55
%S A080249 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 A080249 19215,3321,126,1,1,5461,184275,402591,135450,10377,210,1,1,21845,
%U A080249 1848211,8236095,5143341,716562,28017,330,1,1,87381,18503955,166570111,188253030,45270813,3069990,67617,495,1
%N A080249 Stirling-like number triangle defined by the sequence A000292=C(n+3,3).
%C A080249 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 A080249 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 A080249 Triangle begins:
%e A080249 1;
%e A080249 1,    1;
%e A080249 1,    5,      1;
%e A080249 1,   21,     15,      1;
%e A080249 1,   85,    171,     35,      1;
%e A080249 1,  341,   1795,    871,     70,     1;
%e A080249 1, 1365,  18291,  19215,   3321,   126,   1;
%e A080249 1, 5461, 184275, 402591, 135450, 10377, 210, 1;
%e A080249 For example, 171 = 21+10*15, 35 = 15+20*1.
%Y A080249 Cf. A080248, A008277.
%K A080249 easy,nonn,tabl
%O A080249 0,5
%A A080249 _Paul Barry_, Feb 17 2003

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