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 A193738 Triangular array:  the fusion of polynomial sequences P and Q given by p(n,x)=q(n,x)=x^n+x^(n-1)+...+x+1. 6
 1, 1, 1, 1, 2, 2, 1, 2, 3, 3, 1, 2, 3, 4, 4, 1, 2, 3, 4, 5, 5, 1, 2, 3, 4, 5, 6, 6, 1, 2, 3, 4, 5, 6, 7, 7, 1, 2, 3, 4, 5, 6, 7, 8, 8, 1, 2, 3, 4, 5, 6, 7, 8, 9, 9, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 11, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 12, 1, 2, 3, 4 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS See A193722 for the definition of fusion of two sequences of polynomials or triangular arrays. LINKS Reinhard Zumkeller, Rows n = 0..100 of triangle, flattened EXAMPLE First six rows: 1 1....1 1....2....2 1....2....3....3 1....2....3....4...4 1....2....3....4...5...5 MATHEMATICA z = 12; p[0, x_] := 1 p[n_, x_] := x*p[n - 1, x] + 1; p[n_, 0] := p[n, x] /. x -> 0 q[n_, x_] := p[n, x] t[n_, k_] := Coefficient[p[n, x], x^(n - k)]; t[n_, n_] := p[n, x] /. x -> 0; w[n_, x_] := Sum[t[n, k]*q[n + 1 - k, x], {k, 0, n}]; w[-1, x_] := 1 g[n_] := CoefficientList[w[n, x], {x}] TableForm[Table[Reverse[g[n]], {n, -1, z}]] Flatten[Table[Reverse[g[n]], {n, -1, z}]]  (* A193738 *) TableForm[Table[g[n], {n, -1, z}]] Flatten[Table[g[n], {n, -1, z}]]   (* A193739 *) PROG (Haskell) a193738 n k = a193738_tabl !! n !! k a193738_row n = a193738_tabl !! n a193738_tabl = map reverse a193739_tabl -- Reinhard Zumkeller, May 11 2013 CROSSREFS Cf. A193722, A193739. Sequence in context: A070680 A054711 A241424 * A230494 A134658 A106580 Adjacent sequences:  A193735 A193736 A193737 * A193739 A193740 A193741 KEYWORD nonn,tabl AUTHOR Clark Kimberling, Aug 04 2011 STATUS approved

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