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A209560 Triangle of coefficients of polynomials v(n,x) jointly generated with A209559; see the Formula section. 3
1, 3, 1, 5, 5, 1, 9, 12, 7, 1, 15, 29, 22, 9, 1, 25, 61, 66, 35, 11, 1, 41, 124, 166, 125, 51, 13, 1, 67, 241, 394, 365, 211, 70, 15, 1, 109, 457, 877, 988, 701, 329, 92, 17, 1, 177, 848, 1877, 2472, 2129, 1225, 484, 117, 19, 1, 287, 1549, 3884, 5880, 5909 (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..60.

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

3....1

5....5....1

9....12...7....1

15...29...22...9...1

First three polynomials v(n,x): 1, 3 + x , 5 + 5x + 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. A209559, A208510.

Sequence in context: A111125 A209159 A182397 * A211977 A072919 A273171

Adjacent sequences:  A209557 A209558 A209559 * A209561 A209562 A209563

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 10 2012

STATUS

approved

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Last modified October 21 08:47 EDT 2019. Contains 328292 sequences. (Running on oeis4.)