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%I #3 Mar 30 2012 18:59:07
%S 1,2,1,5,3,1,14,9,4,1,42,29,14,5,1,132,99,50,20,6,1,429,351,186,78,27,
%T 7,1,1430,1275,714,311,114,35,8,1,4862,4707,2796,1271,483,159,44,9,1,
%U 16796,17577,11082,5282,2082,712,214,54,10,1,58786,66197,44250,22160
%N Binomial transform of number triangle A105632.
%C Product of binomial matrix C(n,k) and A105632. Row sums are A105849.
%F Column k has g.f. (sum{j=0..k-1, C(k-1, j)C(j)x^(2j)/(1-4x)^(j+1/2)}+0^k*(1-2x-sqrt(1-4x))/(2x^2))(x/(1-x))^k
%e Triangle begins
%e 1;
%e 2,1;
%e 5,3,1;
%e 14,9,4,1;
%e 42,29,14,5,1;
%e 132,99,50,20,6,1;
%K easy,nonn,tabl
%O 0,2
%A _Paul Barry_, Apr 22 2005
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