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A208914 Triangle of coefficients of polynomials v(n,x) jointly generated with A208913; see the Formula section. 5
1, 2, 2, 3, 4, 4, 4, 6, 16, 8, 5, 8, 40, 32, 16, 6, 10, 80, 80, 96, 32, 7, 12, 140, 160, 336, 192, 64, 8, 14, 224, 280, 896, 672, 512, 128, 9, 16, 336, 448, 2016, 1792, 2304, 1024, 256, 10, 18, 480, 672, 4032, 4032, 7680, 4608, 2560, 512, 11, 20, 660, 960 (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..59.

FORMULA

u(n,x)=u(n-1,x)+2x*v(n-1,x),

v(n,x)=2x*u(n-1,x)+v(n-1,x)+1,

where u(1,x)=1, v(1,x)=1.

EXAMPLE

First five rows:

1

2...2

3...4...4

4...6...16...8

5...8...40...32...16

First five polynomials v(n,x):

1

2 + 2x

3 + 4x + 4x^2

4 + 6x + 16x^2 + 8x^3

5 + 8x + 40x^2 + 32x^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_] := 2 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[%]    (* A208913 *)

Table[Expand[v[n, x]], {n, 1, z}]

cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];

TableForm[cv]

Flatten[%]    (* A208914 *)

CROSSREFS

Cf. A208913, A208510.

Sequence in context: A309559 A130128 A210556 * A049980 A209698 A141525

Adjacent sequences:  A208911 A208912 A208913 * A208915 A208916 A208917

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 03 2012

STATUS

approved

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Last modified October 18 01:04 EDT 2019. Contains 328135 sequences. (Running on oeis4.)