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A167432 Riordan array (c(2x)^2,xc(2x)), c(x) the g.f. of A000108.

%I A167432 #2 Mar 30 2012 18:59:26
%S A167432 1,4,1,20,6,1,112,36,8,1,672,224,56,10,1,4224,1440,384,80,12,1,27456,
%T A167432 9504,2640,600,108,14,1,183040,64064,18304,4400,880,140,16,1,1244672,
%U A167432 439296,128128,32032,6864,1232,176,18,1,8599552,3055104,905216,232960
%N A167432 Riordan array (c(2x)^2,xc(2x)), c(x) the g.f. of A000108.
%C A167432 Inverse of (1-4x+4x^2,x(1-2x)) (A167431). Row sums are A084076. First column is A003645.
%F A167432 Number triangle T(n,k)=A054445(n,k)*2^(n-k).
%e A167432 Triangle begins
%e A167432 1,
%e A167432 4, 1,
%e A167432 20, 6, 1,
%e A167432 112, 36, 8, 1,
%e A167432 672, 224, 56, 10, 1,
%e A167432 4224, 1440, 384, 80, 12, 1,
%e A167432 27456, 9504, 2640, 600, 108, 14, 1,
%e A167432 183040, 64064, 18304, 4400, 880, 140, 16, 1,
%e A167432 1244672, 439296, 128128, 32032, 6864, 1232, 176, 18, 1,
%e A167432 8599552, 3055104, 905216, 232960, 52416, 10192, 1664, 216, 20, 1,
%e A167432 60196864, 21498880, 6449664, 1697280, 396032, 81536, 14560, 2184, 260, 22, 1
%e A167432 The production matrix is
%e A167432 4, 1,
%e A167432 4, 2, 1,
%e A167432 8, 4, 2, 1,
%e A167432 16, 8, 4, 2, 1,
%e A167432 32, 16, 8, 4, 2, 1,
%e A167432 64, 32, 16, 8, 4, 2, 1,
%e A167432 128, 64, 32, 16, 8, 4, 2, 1,
%e A167432 256, 128, 64, 32, 16, 8, 4, 2, 1,
%e A167432 512, 256, 128, 64, 32, 16, 8, 4, 2, 1
%e A167432 When topped with the row (1,0,0,0...), this has inverse
%e A167432 1,
%e A167432 -4, 1,
%e A167432 4, -2, 1,
%e A167432 0, 0, -2, 1,
%e A167432 0, 0, 0, -2, 1,
%e A167432 0, 0, 0, 0, -2, 1,
%e A167432 0, 0, 0, 0, 0, -2, 1,
%e A167432 0, 0, 0, 0, 0, 0, -2, 1,
%e A167432 0, 0, 0, 0, 0, 0, 0, -2, 1,
%e A167432 0, 0, 0, 0, 0, 0, 0, 0, -2, 1
%K A167432 easy,nonn,tabl
%O A167432 0,2
%A A167432 _Paul Barry_, Nov 03 2009