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A208911 Triangle of coefficients of polynomials u(n,x) jointly generated with A208912; see the Formula section. 3
1, 1, 2, 1, 6, 4, 1, 12, 14, 8, 1, 20, 32, 38, 16, 1, 30, 60, 110, 90, 32, 1, 42, 100, 250, 300, 214, 64, 1, 56, 154, 490, 770, 826, 490, 128, 1, 72, 224, 868, 1680, 2408, 2128, 1110, 256, 1, 90, 312, 1428, 3276, 5880, 6888, 5382, 2474, 512, 1, 110, 420 (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..58.

FORMULA

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

1...2

1...6....4

1...12...14...8

1...20...32...38...16

First five polynomials u(n,x):

1

1 + 2x

1 + 6x + 4x^2

1 + 12x + 14x^2 + 8x^3

1 + 20x + 32x^2 + 38x^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 + 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[%]    (* A208911 *)

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

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

TableForm[cv]

Flatten[%]    (* A208912 *)

CROSSREFS

Cf. A208912, A208510.

Sequence in context: A208923 A185045 A208913 * A208761 A123519 A167024

Adjacent sequences:  A208908 A208909 A208910 * A208912 A208913 A208914

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 03 2012

STATUS

approved

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Last modified October 19 04:40 EDT 2019. Contains 328211 sequences. (Running on oeis4.)