A117375 Riordan array (1/(1-3x*c(x)),xc(x)), c(x) the g.f. of A000108.
1, 3, 1, 12, 4, 1, 51, 17, 5, 1, 222, 74, 23, 6, 1, 978, 326, 104, 30, 7, 1, 4338, 1446, 468, 142, 38, 8, 1, 19323, 6441, 2103, 657, 189, 47, 9, 1, 86310, 28770, 9447, 3006, 903, 246, 57, 10, 1, 386250, 128750, 42440, 13670, 4223, 1217, 314, 68, 11, 1, 1730832
Offset: 0
Examples
Triangle begins 1, 3, 1, 12, 4, 1, 51, 17, 5, 1, 222, 74, 23, 6, 1, 978, 326, 104, 30, 7, 1, 4338, 1446, 468, 142, 38, 8, 1 Production array begins 3, 1 3, 1, 1 3, 1, 1, 1 3, 1, 1, 1, 1 3, 1, 1, 1, 1, 1 3, 1, 1, 1, 1, 1, 1 3, 1, 1, 1, 1, 1, 1, 1 3, 1, 1, 1, 1, 1, 1, 1, 1 ... - _Philippe Deléham_, Mar 05 2013
Formula
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)}
Comments