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A208905 Triangle of coefficients of polynomials u(n,x) jointly generated with A208906; see the Formula section. 3
1, 1, 2, 1, 6, 2, 1, 12, 6, 4, 1, 20, 12, 20, 4, 1, 30, 20, 60, 20, 8, 1, 42, 30, 140, 60, 56, 8, 1, 56, 42, 280, 140, 224, 56, 16, 1, 72, 56, 504, 280, 672, 224, 144, 16, 1, 90, 72, 840, 504, 1680, 672, 720, 144, 32, 1, 110, 90, 1320, 840, 3696, 1680, 2640, 720 (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..64.

FORMULA

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

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

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

EXAMPLE

First five rows:

1

1...2

1...6....2

1...12...6....4

1...20...12...20...4

First five polynomials u(n,x):

1

1 + 2x

1 + 6x + 2x^2

1 + 12x + 6x^2 + 4x^3

1 + 20x + 12x^2 + 20x^3 + 4x^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] + 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[%]  (* A208905 *)

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

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

TableForm[cv]

Flatten[%]  (* A208906 *)

CROSSREFS

Cf. A208906, A208510.

Sequence in context: A030304 A248779 A286030 * A208749 A208751 A133200

Adjacent sequences:  A208902 A208903 A208904 * A208906 A208907 A208908

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 03 2012

STATUS

approved

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Last modified October 15 13:06 EDT 2019. Contains 328030 sequences. (Running on oeis4.)