OFFSET
0,2
COMMENTS
See A193722 for the definition of fusion of two sequences of polynomials or triangular arrays.
First five rows of P, from coefficients of p(n,x):
1
1...2
1...2...4
1...2...4...8
1...2...4...8...16
First five rows of Q, from coefficients of q(n,x):
1
2...1
4...2...1
8...4...2...1
16..8...4...2..1
EXAMPLE
First six rows of A193904:
1
2....1
8....6....3
32...24...14...7
128..96...56...30...15
512..384..224..120..62..31
MATHEMATICA
z = 12;
p[n_, x_] := x*p[n - 1, x] + 2^n; p[0, x_] := 1;
q[n_, x_] := 2 x*q[n - 1, x] + 1; q[0, x_] := 1;
t[n_, k_] := Coefficient[p[n, x], x^k]; t[n_, 0] := 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}]] (* A193904 *)
TableForm[Table[g[n], {n, -1, z}]]
Flatten[Table[g[n], {n, -1, z}]] (* A193905 *)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Aug 08 2011
STATUS
approved