A208912 - OEIS

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A208912

Triangle of coefficients of polynomials v(n,x) jointly generated with A208911; see the Formula section.

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:

2...2

3...5....3

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

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

First five polynomials v(n,x):

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