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A208917
Triangle of coefficients of polynomials u(n,x) jointly generated with A208918; see the Formula section.
3
1, 1, 2, 1, 4, 8, 1, 6, 16, 24, 1, 8, 24, 56, 80, 1, 10, 32, 96, 208, 256, 1, 12, 40, 144, 384, 736, 832, 1, 14, 48, 200, 608, 1472, 2624, 2688, 1, 16, 56, 264, 880, 2496, 5632, 9216, 8704, 1, 18, 64, 336, 1200, 3840, 10112, 21120, 32256, 28160, 1, 20, 72
OFFSET
1,3
COMMENTS
For a discussion and guide to related arrays, see A208510.
FORMULA
u(n,x)=u(n-1,x)+2x*v(n-1,x),
v(n,x)=2x*u(n-1,x)+2x*v(n-1,x)+1,
where u(1,x)=1, v(1,x)=1.
EXAMPLE
First five rows:
1
1...2
1...4...8
1...6...16...24
1...8...24...56...80
First five polynomials u(n,x):
1
1 + 2x
1 + 4x + 8x^2
1 + 6x + 16x^2 + 24x^3
1 + 8x + 24x^2 + 56x^3 + 80x^4
MATHEMATICA
u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := u[n - 1, x] + 2 x*v[n - 1, x];
v[n_, x_] := 2 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[%] (* A208917 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%] (* A208918 *)
CROSSREFS
Sequence in context: A038557 A348678 A011234 * A161381 A220579 A330787
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Mar 04 2012
STATUS
approved