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%I #2 Mar 30 2012 18:59:20
%S 1,2,1,12,8,1,80,60,12,1,560,448,112,16,1,4032,3360,960,180,20,1,
%T 29568,25344,7920,1760,264,24,1,219648,192192,64064,16016,2912,364,28,
%U 1,1647360,1464320,512512,139776,29120,4480,480,32,1,12446720
%N Inverse of number triangle A128412.
%C First column is A069723.
%F Number triangle T(n,k)=if(k=0,2^n*(C(2n,n)/2+0^n/2),2^(n-k)*C(2n,n-k)); Column k has g.f. if(k=0,4x/(sqrt(1-8x)(1-sqrt(1-8x))),(1/sqrt(1-8x))*((1-4x-sqrt(1-8x))/(8x))^k);
%e Triangle begins
%e 1,
%e 2, 1,
%e 12, 8, 1,
%e 80, 60, 12, 1,
%e 560, 448, 112, 16, 1,
%e 4032, 3360, 960, 180, 20, 1,
%e 29568, 25344, 7920, 1760, 264, 24, 1,
%e 219648, 192192, 64064, 16016, 2912, 364, 28, 1
%Y Cf. A128417.
%K easy,nonn,tabl
%O 0,2
%A _Paul Barry_, Mar 02 2007
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