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A209698 Triangle of coefficients of polynomials v(n,x) jointly generated with A209697; see the Formula section. 3
1, 2, 2, 3, 4, 4, 4, 7, 10, 8, 5, 11, 20, 24, 16, 6, 16, 35, 54, 56, 32, 7, 22, 56, 104, 140, 128, 64, 8, 29, 84, 181, 294, 352, 288, 128, 9, 37, 120, 293, 552, 800, 864, 640, 256, 10, 46, 165, 449, 957, 1610, 2112, 2080, 1408, 512, 11, 56, 220, 659, 1562 (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..60.

FORMULA

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

v(n,x)=x*u(n-1,x)+(x+1)*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...7....10...8

5...11...20...24...16

First three polynomials v(n,x): 1, 2 + 2x , 3 + 4x + 4x^2.

MATHEMATICA

u[1, x_] := 1; v[1, x_] := 1; z = 16;

u[n_, x_] := x*u[n - 1, x] + x*v[n - 1, x];

v[n_, x_] := x*u[n - 1, x] + (x + 1)*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[%]   (* A209697 *)

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

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

TableForm[cv]

Flatten[%]   (* A209698 *)

CROSSREFS

Cf. A209697, A208510.

Sequence in context: A210556 A208914 A049980 * A141525 A209764 A071475

Adjacent sequences:  A209695 A209696 A209697 * A209699 A209700 A209701

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 12 2012

STATUS

approved

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Last modified October 17 10:03 EDT 2019. Contains 328107 sequences. (Running on oeis4.)