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A117380 Riordan array (1/(1-4*x*c(x)),xc(x)), c(x) the g.f. of A000108.

%I A117380 #6 Mar 05 2013 15:57:53
%S A117380 1,4,1,20,5,1,104,26,6,1,548,137,33,7,1,2904,726,178,41,8,1,15432,
%T A117380 3858,954,228,50,9,1,82128,20532,5100,1242,288,60,10,1,437444,109361,
%U A117380 27233,6701,1601,359,71,11,1,2331128,582782,145338,35977,8744,2043,442,83,12
%N A117380 Riordan array (1/(1-4*x*c(x)),xc(x)), c(x) the g.f. of A000108.
%C A117380 Triangle factors as (1,xc(x))*(1/(1-4x),x). Inverse of A117377. First row is A076035. Second row is A076025(n)-0^n. Row sums are A076025(n+1). Diagonal sums are A117381.
%F A117380 Number triangle T(0,0)=1, T(n,k)=[k<=n]*sum{j=0..n, (j/(n-j))*C(2n-j,n-j)[k<=j]*4^(j-k)}
%e A117380 Triangle begins
%e A117380 1,
%e A117380 4, 1,
%e A117380 20, 5, 1,
%e A117380 104, 26, 6, 1,
%e A117380 548, 137, 33, 7, 1,
%e A117380 2904, 726, 178, 41, 8, 1
%e A117380 Production array begins
%e A117380 4, 1
%e A117380 4, 1, 1
%e A117380 4, 1, 1, 1
%e A117380 4, 1, 1, 1, 1
%e A117380 4, 1, 1, 1, 1, 1
%e A117380 4, 1, 1, 1, 1, 1, 1
%e A117380 4, 1, 1, 1, 1, 1, 1, 1
%e A117380 4, 1, 1, 1, 1, 1, 1, 1, 1
%e A117380 ... - _Philippe Deléham_, Mar 05 2013
%K A117380 easy,nonn,tabl
%O A117380 0,2
%A A117380 _Paul Barry_, Mar 10 2006