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A208521 Triangle of coefficients of polynomials v(n,x) jointly generated with A208520; see the Formula section. 3
1, 2, 2, 3, 4, 2, 4, 6, 8, 4, 5, 8, 20, 16, 4, 6, 10, 40, 40, 24, 8, 7, 12, 70, 80, 84, 48, 8, 8, 14, 112, 140, 224, 168, 64, 16, 9, 16, 168, 224, 504, 448, 288, 128, 16, 10, 18, 240, 336, 1008, 1008, 960, 576, 160, 32, 11, 20, 330, 480, 1848, 2016, 2640, 1920 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..63.

FORMULA

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

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

5...8...20...16...4

First five polynomials v(n,x):

1

2 + 2x

3 + 4x + 2x^2

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

5 + 8x + 20x^2 + 16x^3 + 4x^4

MATHEMATICA

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

u[n_, x_] := u[n - 1, x] + 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[%]    (* A208520 *)

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

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

TableForm[cv]

Flatten[%]    (* A208521 *)

CROSSREFS

Cf. A208520.

Sequence in context: A290600 A143595 A211702 * A209570 A205703 A325785

Adjacent sequences:  A208518 A208519 A208520 * A208522 A208523 A208524

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Feb 28 2012

STATUS

approved

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Last modified August 18 08:57 EDT 2019. Contains 326077 sequences. (Running on oeis4.)