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A208906 Triangle of coefficients of polynomials v(n,x) jointly generated with A208905; see the Formula section. 3
1, 2, 1, 3, 2, 2, 4, 3, 8, 2, 5, 4, 20, 8, 4, 6, 5, 40, 20, 24, 4, 7, 6, 70, 40, 84, 24, 8, 8, 7, 112, 70, 224, 84, 64, 8, 9, 8, 168, 112, 504, 224, 288, 64, 16, 10, 9, 240, 168, 1008, 504, 960, 288, 160, 16, 11, 10, 330, 240, 1848, 1008, 2640, 960, 880, 160, 32 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

For a discussion and guide to related arrays, see A208510.

LINKS

Table of n, a(n) for n=1..66.

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

2...1

3...2...2

4...3...8....2

5...4...20...8...4

First five polynomials v(n,x):

1

2 + x

3 + 2x + 2x^2

4 + 3x + 8x^2 + 2x^3

5 + 4x + 20x^2 + 8x^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

Cf. A208905, A208510.

Sequence in context: A137948 A210553 A269456 * A120933 A209756 A210795

Adjacent sequences:  A208903 A208904 A208905 * A208907 A208908 A208909

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 03 2012

STATUS

approved

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Last modified October 22 19:53 EDT 2019. Contains 328319 sequences. (Running on oeis4.)