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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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

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

LINKS

Table of n, a(n) for n=1..62.

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

Cf. A208756, A208510.

Sequence in context: A105537 A115237 A105542 * A200057 A136600 A136672

Adjacent sequences:  A208904 A208905 A208906 * A208908 A208909 A208910

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 03 2012

STATUS

approved

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Last modified October 17 08:36 EDT 2019. Contains 328107 sequences. (Running on oeis4.)