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A209771 Triangle of coefficients of polynomials u(n,x) jointly generated with A209772; see the Formula section. 3
1, 1, 2, 2, 5, 4, 2, 9, 14, 8, 3, 14, 32, 36, 16, 3, 20, 60, 100, 88, 32, 4, 27, 100, 220, 288, 208, 64, 4, 35, 154, 420, 728, 784, 480, 128, 5, 44, 224, 728, 1568, 2240, 2048, 1088, 256, 5, 54, 312, 1176, 3024, 5376, 6528, 5184, 2432, 512, 6, 65, 420 (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..58.

FORMULA

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

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

where u(1,x)=1, v(1,x)=1.

EXAMPLE

First five rows:

1

1...2

2...5....4

2...9....14...8

3...14...32...36...16

First three polynomials u(n,x): 1, 1 + 2x, 2 + 5x + 4x^2.

MATHEMATICA

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

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

v[n_, x_] := (x + 1)*u[n - 1, x] + x*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[%] (* A209771 *)

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

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

TableForm[cv]

Flatten[%] (* A209772 *)

CROSSREFS

Cf. A209772, A208510.

Sequence in context: A135281 A068465 A217876 * A209751 A275381 A283235

Adjacent sequences: A209768 A209769 A209770 * A209772 A209773 A209774

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 15 2012

STATUS

approved

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Last modified November 28 17:22 EST 2022. Contains 358421 sequences. (Running on oeis4.)