%I A154559
%S A154559 1,2,0,3,2,0,4,6,4,0,5,12,16,9,0,6,20,40,45,21,0,7,30,80,135,126,51,0,
               8,
%T A154559 42,140,315,441,357,127,0,9,56,224,630,1176,1428,1016,323,0,10,72,336,
%U A154559 1134,2646,4284,4572,2907,835,0
%N A154559 Triangle read by rows, A007318 * (A129186 * (A001006 * 0^(n-k))
%C A154559 Row sums = the Catalan numbers, A000108, starting with offset 1:
%C A154559 (1, 2, 5, 14, 42,...).
%F A154559 Triangle read by rows, A007318 * (A129186 * (A001006 * 0^(n-k))
%F A154559 Binomial transform of a bidiagonal matrix with (1,0,0,0,..,.) as the 
               main
%F A154559 diagonal and A001006 as the subddiagonal starting (1, 2, 4, 9, 21, 51,
               ...).
%e A154559 First few rows of the triangle =
%e A154559 1;
%e A154559 2, 0;
%e A154559 3, 2, 0;
%e A154559 4, 6, 4, 0;
%e A154559 5, 12, 16, 9, 0;
%e A154559 6, 20, 40, 45, 21, 0;
%e A154559 7, 30, 80, 135, 126, 51, 0;
%e A154559 8, 42, 140, 315, 441, 357, 127, 0;
%e A154559 9, 56, 224, 630, 1176, 1428, 1016, 323, 0;
%e A154559 10, 72, 336, 1134, 2646, 4284, 4572, 2907, 835, 0;
%e A154559 11, 90, 480, 1890, 5292, 10710, 15240, 14535, 8350, 2188;
%e A154559 12, 110, 660, 2970, 9702, 23562, 41910, 53295, 45925, 24068, 5798;
%e A154559 ...
%Y A154559 Cf. A001006, A000108
%Y A154559 Sequence in context: A127479 A141432 A115241 this_sequence A143324 A097418 
               A154752
%Y A154559 Adjacent sequences: A154556 A154557 A154558 this_sequence A154560 A154561 
               A154562
%K A154559 nonn,tabl
%O A154559 1,2
%A A154559 Gary W. Adamson (qntmpkt(AT)yahoo.com), Jan 11 2009