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A208905
Triangle of coefficients of polynomials u(n,x) jointly generated with A208906; see the Formula section.
3
1, 1, 2, 1, 6, 2, 1, 12, 6, 4, 1, 20, 12, 20, 4, 1, 30, 20, 60, 20, 8, 1, 42, 30, 140, 60, 56, 8, 1, 56, 42, 280, 140, 224, 56, 16, 1, 72, 56, 504, 280, 672, 224, 144, 16, 1, 90, 72, 840, 504, 1680, 672, 720, 144, 32, 1, 110, 90, 1320, 840, 3696, 1680, 2640, 720
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)=x*u(n-1,x)+v(n-1,x)+1,
where u(1,x)=1, v(1,x)=1.
EXAMPLE
First five rows:
1
1...2
1...6....2
1...12...6....4
1...20...12...20...4
First five polynomials u(n,x):
1
1 + 2x
1 + 6x + 2x^2
1 + 12x + 6x^2 + 4x^3
1 + 20x + 12x^2 + 20x^3 + 4x^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_] := x*u[n - 1, 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[%] (* A208905 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%] (* A208906 *)
CROSSREFS
Sequence in context: A248779 A286030 A343684 * A208749 A208751 A133200
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Mar 03 2012
STATUS
approved