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
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Aug 04 2011
STATUS
approved