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A209752
Triangle of coefficients of polynomials v(n,x) jointly generated with A209751; see the Formula section.
3
1, 2, 2, 2, 6, 4, 3, 9, 16, 8, 3, 16, 33, 40, 16, 4, 20, 67, 105, 96, 32, 4, 30, 103, 242, 305, 224, 64, 5, 35, 169, 441, 793, 833, 512, 128, 5, 48, 230, 792, 1664, 2424, 2177, 1152, 256, 6, 54, 338, 1230, 3272, 5736, 7031, 5505, 2560, 512, 6, 70, 430
OFFSET
1,2
COMMENTS
For a discussion and guide to related arrays, see A208510.
FORMULA
u(n,x)=x*u(n-1,x)+(x+1)*v(n-1,x),
v(n,x)=u(n-1,x)+2x*v(n-1,x)+1,
where u(1,x)=1, v(1,x)=1.
EXAMPLE
First five rows:
1
2...2
2...6....4
3...9....16...8
3...16...33...40...16
First three polynomials v(n,x): 1, 2 + 2x , 2 + 6x + 4x^2.
MATHEMATICA
u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := x*u[n - 1, x] + (x + 1)*v[n - 1, x];
v[n_, x_] := u[n - 1, x] + 2 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[%] (* A209751 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%] (* A209752 *)
CROSSREFS
Sequence in context: A053695 A210550 A208659 * A119918 A084867 A194949
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Mar 14 2012
STATUS
approved