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A209752 Triangle of coefficients of polynomials v(n,x) jointly generated with A209751; see the Formula section. 3
1, 2, 2, 2, 6, 4, 3, 9, 16, 8, 3, 16, 33, 40, 16, 4, 20, 67, 105, 96, 32, 4, 30, 103, 242, 305, 224, 64, 5, 35, 169, 441, 793, 833, 512, 128, 5, 48, 230, 792, 1664, 2424, 2177, 1152, 256, 6, 54, 338, 1230, 3272, 5736, 7031, 5505, 2560, 512, 6, 70, 430 (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..58.

FORMULA

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

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

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

EXAMPLE

First five rows:

1

2...2

2...6....4

3...9....16...8

3...16...33...40...16

First three polynomials v(n,x): 1, 2 + 2x , 2 + 6x + 4x^2.

MATHEMATICA

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

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

v[n_, x_] := u[n - 1, x] + 2 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[%]    (* A209751 *)

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

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

TableForm[cv]

Flatten[%]    (* A209752 *)

CROSSREFS

Cf. A209651, A208510.

Sequence in context: A053695 A210550 A208659 * A119918 A084867 A194949

Adjacent sequences:  A209749 A209750 A209751 * A209753 A209754 A209755

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 14 2012

STATUS

approved

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Last modified September 21 00:17 EDT 2019. Contains 327252 sequences. (Running on oeis4.)