OFFSET
0,3
FORMULA
EXAMPLE
First six rows:
1
1....2
3....6....8
7....14...24....32
15...30...56....96....128
31...62...120...224...384...512
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