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%I #5 Mar 30 2012 18:57:38
%S 1,1,3,1,8,19,1,15,80,172,1,24,221,971,1967,1,35,492,3547,13809,26832,
%T 1,48,955,10186,62840,224529,422609,1,63,1684,24890,222132,1226003,
%U 4102449,7525966,1,80,2765,54077,658319,5167948,26193697,83159133
%N Augmentation of the triangle A122366. See Comments.
%C For an introduction to the unary operation "augmentation" as applied to triangular arrays or sequences of polynomials, see A193091.
%e First five rows of A193602:
%e 1
%e 1...3
%e 1...8....19
%e 1...15...80...172
%e 1...24...221..971...1967
%t p[n_, k_] := Binomial[2 n + 1, k] (* A122366 *)
%t Table[p[n, k], {n, 0, 7}, {k, 0, n}]
%t m[n_] := Table[If[i <= j, p[n + 1 - i, j - i], 0], {i, n}, {j, n + 1}]
%t TableForm[m[4]]
%t w[0, 0] = 1; w[1, 0] = p[1, 0]; w[1, 1] = p[1, 1];
%t v[0] = w[0, 0]; v[1] = {w[1, 0], w[1, 1]};
%t v[n_] := v[n - 1].m[n]
%t TableForm[Table[v[n], {n, 0, 6}]] (* A193602 *)
%t Flatten[Table[v[n], {n, 0, 8}]]
%Y Cf. A122366, A193091.
%K nonn,tabl
%O 0,3
%A _Clark Kimberling_, Jul 31 2011
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