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A209559 Triangle of coefficients of polynomials u(n,x) jointly generated with A209560; see the Formula section. 4
1, 1, 1, 3, 2, 1, 5, 8, 3, 1, 9, 17, 15, 4, 1, 15, 38, 39, 24, 5, 1, 25, 76, 104, 74, 35, 6, 1, 41, 149, 242, 229, 125, 48, 7, 1, 67, 282, 543, 607, 440, 195, 63, 8, 1, 109, 524, 1159, 1531, 1308, 769, 287, 80, 9, 1, 177, 957, 2401, 3631, 3660, 2533, 1253, 404 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

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

LINKS

Table of n, a(n) for n=1..63.

FORMULA

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

v(n,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...1

3...2....1

5...8....3....1

9...17...15...4...1

First three polynomials v(n,x): 1, 1 + x, 3 + 2x + x^2.

MATHEMATICA

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

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

v[n_, 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[%]   (* A209559 *)

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

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

TableForm[cv]

Flatten[%]   (* A209560 *)

CROSSREFS

Cf. A209560, A208510.

Sequence in context: A208511 A129675 A232206 * A081277 A079628 A140287

Adjacent sequences:  A209556 A209557 A209558 * A209560 A209561 A209562

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 10 2012

STATUS

approved

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Last modified October 20 07:23 EDT 2019. Contains 328252 sequences. (Running on oeis4.)