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A209701 Triangle of coefficients of polynomials u(n,x) jointly generated with A209702; see the Formula section. 3
1, 0, 2, 0, 2, 5, 0, 3, 7, 12, 0, 4, 11, 23, 29, 0, 5, 16, 41, 70, 70, 0, 6, 22, 66, 140, 204, 169, 0, 7, 29, 99, 247, 455, 577, 408, 0, 8, 37, 141, 401, 875, 1423, 1597, 985, 0, 9, 46, 193, 613, 1529, 2965, 4321, 4348, 2378, 0, 10, 56, 256, 895, 2495, 5549 (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)=x*u(n-1,x)+x*v(n-1,x),

v(n,x)=2x*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

0...2

0...2...5

0...3...7....12

0...4...11...23...29

First three polynomials v(n,x): 1, 2x, 2x + 5x^2.

MATHEMATICA

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

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

v[n_, x_] := 2 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[%]  (* A209701 *)

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

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

TableForm[cv]

Flatten[%]  (* A209702 *)

CROSSREFS

Cf. A209702, A208510.

Sequence in context: A279327 A052438 A324045 * A158855 A005074 A161564

Adjacent sequences:  A209698 A209699 A209700 * A209702 A209703 A209704

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 12 2012

STATUS

approved

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Last modified October 22 14:44 EDT 2019. Contains 328318 sequences. (Running on oeis4.)