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A210224
Triangle of coefficients of polynomials v(n,x) jointly generated with A210223; see the Formula section.
3
1, 1, 3, 1, 5, 5, 1, 5, 15, 7, 1, 5, 19, 35, 9, 1, 5, 19, 63, 69, 11, 1, 5, 19, 71, 177, 121, 13, 1, 5, 19, 71, 249, 429, 195, 15, 1, 5, 19, 71, 265, 781, 923, 295, 17, 1, 5, 19, 71, 265, 957, 2171, 1807, 425, 19, 1, 5, 19, 71, 265, 989, 3211, 5407, 3281, 589, 21
OFFSET
1,3
COMMENTS
Limiting row: A001834
For a discussion and guide to related arrays, see A208510.
FORMULA
u(n,x)=x*u(n-1,x)+v(n-1,x)+1,
v(n,x)=2x*u(n-1,x)+x*v(n-1,x)+1,
where u(1,x)=1, v(1,x)=1.
EXAMPLE
First five rows:
1
1...3
1...5...5
1...5...15...7
1...5...19...35...9
First three polynomials v(n,x): 1, 1 + 3x , 1 + 5x + 5x^2.
MATHEMATICA
u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := x*u[n - 1, x] + v[n - 1, x] + 1;
v[n_, x_] := 2 x*u[n - 1, x] + x*v[n - 1, x] + 1;
Table[Expand[u[n, x]], {n, 1, z/2}]
Table[Expand[v[n, x]], {n, 1, z/2}]
cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
TableForm[cu]
Flatten[%] (* A210223 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%] (* A210224 *)
CROSSREFS
Sequence in context: A351965 A228785 A135184 * A131304 A131302 A131305
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Mar 20 2012
STATUS
approved