%I #6 Mar 05 2013 15:58:16

%S 1,3,1,12,4,1,51,17,5,1,222,74,23,6,1,978,326,104,30,7,1,4338,1446,

%T 468,142,38,8,1,19323,6441,2103,657,189,47,9,1,86310,28770,9447,3006,

%U 903,246,57,10,1,386250,128750,42440,13670,4223,1217,314,68,11,1,1730832

%N Riordan array (1/(1-3x*c(x)),xc(x)), c(x) the g.f. of A000108.

%C Triangle factors as (1,xc(x))*(1/(1-3x),x). First row is A007854. Second row is A049027(n)-0^n. Row sums are A049027(n+1). Diagonal sums are A117376.

%F 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]*3^(j-k)}

%e Triangle begins

%e 1,

%e 3, 1,

%e 12, 4, 1,

%e 51, 17, 5, 1,

%e 222, 74, 23, 6, 1,

%e 978, 326, 104, 30, 7, 1,

%e 4338, 1446, 468, 142, 38, 8, 1

%e Production array begins

%e 3, 1

%e 3, 1, 1

%e 3, 1, 1, 1

%e 3, 1, 1, 1, 1

%e 3, 1, 1, 1, 1, 1

%e 3, 1, 1, 1, 1, 1, 1

%e 3, 1, 1, 1, 1, 1, 1, 1

%e 3, 1, 1, 1, 1, 1, 1, 1, 1

%e ... - _Philippe Deléham_, Mar 05 2013

%K easy,nonn,tabl

%O 0,2

%A _Paul Barry_, Mar 10 2006