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A193601 Augmentation of the triangle A062344. See Comments.

%I A193601 #8 Jun 28 2017 19:36:12
%S A193601 1,1,2,1,6,10,1,12,49,76,1,20,149,508,756,1,30,354,2082,6353,9192,1,
%T A193601 42,720,6484,32852,92750,131406,1,56,1315,16820,127365,580606,1545757,
%U A193601 2153912,1,72,2219,38256,404559,2706150,11385058,28931758,39768798
%N A193601 Augmentation of the triangle A062344.  See Comments.
%C A193601 For an introduction to the unary operation "augmentation" as applied to triangular arrays or sequences of polynomials, see A193091.
%e A193601 First 5 rows of A193601:
%e A193601 1
%e A193601 1...2
%e A193601 1...6....10
%e A193601 1...12...49...76
%e A193601 1...20...149..508...756
%t A193601 p[n_, k_] := Binomial[2 n, k] (* A062344 *)
%t A193601 Table[p[n, k], {n, 0, 5}, {k, 0, n}]
%t A193601 m[n_] := Table[If[i <= j, p[n + 1 - i, j - i], 0], {i, n}, {j, n + 1}]
%t A193601 TableForm[m[4]]
%t A193601 w[0, 0] = 1; w[1, 0] = p[1, 0]; w[1, 1] = p[1, 1];
%t A193601 v[0] = w[0, 0]; v[1] = {w[1, 0], w[1, 1]};
%t A193601 v[n_] := v[n - 1].m[n]
%t A193601 TableForm[Table[v[n], {n, 0, 6}]] (* A193601 *)
%t A193601 Flatten[Table[v[n], {n, 0, 8}]]
%Y A193601 Cf. A193091, A062344.
%K A193601 nonn,tabl
%O A193601 0,3
%A A193601 _Clark Kimberling_, Jul 31 2011