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A193604 Augmentation of the triangle A055248. See Comments.

%I A193604 #5 Mar 30 2012 18:57:38
%S A193604 1,2,1,8,8,3,64,88,62,19,1024,1664,1568,896,233,32768,58368,64128,
%T A193604 49248,23890,5385,2097152,3932160,4703232,4249728,2800488,1179656,
%U A193604 233787,268435456,517996544,649887744,645547008,507802304,293645688,108978862
%N A193604 Augmentation of the triangle A055248.  See Comments.
%C A193604 For an introduction to the unary operation "augmentation" as applied to triangular arrays or sequences of polynomials, see A193091.
%e A193604 First five rows of A193604:
%e A193604 1
%e A193604 2.....1
%e A193604 8.....8.....3
%e A193604 64....88....62....19
%e A193604 1024..1664..1568..896...233
%t A193604 u[n_, k_] := Sum[Binomial[n, h], {h, 0, k}] (* A055248 *)
%t A193604 p[n_, k_] := u[n, n - k]
%t A193604 Table[p[n, k], {n, 0, 5}, {k, 0, n}]
%t A193604 m[n_] := Table[If[i <= j, p[n + 1 - i, j - i], 0], {i, n}, {j, n + 1}]
%t A193604 TableForm[m[4]]
%t A193604 w[0, 0] = 1; w[1, 0] = p[1, 0]; w[1, 1] = p[1, 1];
%t A193604 v[0] = w[0, 0]; v[1] = {w[1, 0], w[1, 1]};
%t A193604 v[n_] := v[n - 1].m[n]
%t A193604 TableForm[Table[v[n], {n, 0, 6}]] (* A193604 *)
%t A193604 Flatten[Table[v[n], {n, 0, 8}]]
%Y A193604 Cf. A055248, A193091.
%K A193604 nonn,tabl
%O A193604 0,2
%A A193604 _Clark Kimberling_, Jul 31 2011