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A208912 Triangle of coefficients of polynomials v(n,x) jointly generated with A208911; see the Formula section. 3
1, 2, 2, 3, 5, 4, 4, 9, 15, 8, 5, 14, 36, 37, 16, 6, 20, 70, 105, 91, 32, 7, 27, 120, 235, 306, 213, 64, 8, 35, 189, 455, 791, 819, 491, 128, 9, 44, 280, 798, 1736, 2380, 2136, 1109, 256, 10, 54, 396, 1302, 3402, 5796, 6924, 5373, 2475, 512, 11, 65, 540 (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)=u(n-1,x)+2x*v(n-1,x),

v(n,x)=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

2...2

3...5....3

4...9....15...8

5...14...36...37...16

First five polynomials v(n,x):

1

2 + 2x

3 + 5x + 3x^2

4 + 9x + 15x^2 + 8x^3

5 + 14x + 36x^2 + 37x^3 + 16x^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] + (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[%]    (* A208911 *)

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

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

TableForm[cv]

Flatten[%]    (* A208912 *)

CROSSREFS

Cf. A208911, A208510.

Sequence in context: A243970 A282443 A210554 * A210212 A209762 A026408

Adjacent sequences:  A208909 A208910 A208911 * A208913 A208914 A208915

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 03 2012

STATUS

approved

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Last modified October 15 17:24 EDT 2019. Contains 328037 sequences. (Running on oeis4.)