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A208907
Triangle of coefficients of polynomials u(n,x) jointly generated with A208756; see the Formula section.
2
1, 1, 2, 1, 4, 4, 1, 6, 8, 8, 1, 8, 12, 20, 16, 1, 10, 16, 36, 44, 32, 1, 12, 20, 56, 84, 100, 64, 1, 14, 24, 80, 136, 212, 220, 128, 1, 16, 28, 108, 200, 376, 500, 484, 256, 1, 18, 32, 140, 276, 600, 936, 1188, 1052, 512, 1, 20, 36, 176, 364, 892, 1560
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)+x*v(n-1,x)+1,
where u(1,x)=1, v(1,x)=1.
EXAMPLE
First five rows:
1
1...2
1...4...4
1...6...8....8
1...8...12...20...16
First five polynomials u(n,x):
1
1 + 2x
1 + 4x + 4x^2
1 + 6x + 8x^2 + 8x^3
1 + 8x + 12x^2 + 20x^3 + 16x^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] + 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[%] (* A208907 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%] (* A208756 *)
CROSSREFS
Sequence in context: A105537 A115237 A105542 * A200057 A136600 A136672
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Mar 03 2012
STATUS
approved