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Riordan array [(1-x)exp(x/(1-x)),x]
1

%I #2 Mar 30 2012 18:59:21

%S 1,0,1,1,0,1,4,3,0,1,21,16,6,0,1,136,105,40,10,0,1,1045,816,315,80,15,

%T 0,1,9276,7315,2856,735,140,21,0,1,93289,74208,29260,7616,1470,224,28,

%U 0,1,1047376,839601,333936,87780,17136,2646,336,36

%N Riordan array [(1-x)exp(x/(1-x)),x]

%C First column is essentially A052852.

%e Triangle begins

%e 1,

%e 0, 1,

%e 1, 0, 1,

%e 4, 3, 0, 1,

%e 21, 16, 6, 0, 1,

%e 136, 105, 40, 10, 0, 1,

%e 1045, 816, 315, 80, 15, 0, 1,

%e 9276, 7315, 2856, 735, 140, 21, 0, 1,

%e with production matrix which begins

%e 0, 1,

%e 1, 0, 1,

%e 4, 2, 0, 1,

%e 18, 12, 3, 0, 1,

%e 96, 72, 24, 4, 0, 1,

%e 600, 480, 180, 40, 5, 0, 1;

%e 4320, 3600, 1440, 360, 60, 6, 1

%e with e.g.f. exp(x*t)(t+1/(1-x)^2).

%K easy,nonn,tabl

%O 0,7

%A _Paul Barry_, Nov 26 2008