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A208919 Triangle of coefficients of polynomials u(n,x) jointly generated with A208920; see the Formula section. 3
1, 1, 2, 1, 6, 6, 1, 12, 20, 14, 1, 20, 44, 66, 38, 1, 30, 80, 190, 208, 94, 1, 42, 130, 430, 678, 622, 246, 1, 56, 196, 840, 1708, 2380, 1852, 622, 1, 72, 280, 1484, 3668, 6888, 7928, 5338, 1606, 1, 90, 384, 2436, 7056, 16716, 25344, 25650, 15336 (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..54.

FORMULA

u(n,x)=u(n-1,x)+2x*v(n-1,x),

v(n,x)=2x*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...2

1...6....6

1...12...20...14

1...20...44...66...38

First five polynomials u(n,x):

1

1 + 2x

1 + 6x + 6x^2

1 + 12x + 20x^2 + 14x^3

1 + 20x + 44x^2 + 66x^3 + 38x^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_] := 2 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[%]    (* A208919 *)

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

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

TableForm[cv]

Flatten[%]    (* A208920 *)

CROSSREFS

Cf. A208920, A208510.

Sequence in context: A208909 A229565 A259477 * A259569 A046651 A063007

Adjacent sequences:  A208916 A208917 A208918 * A208920 A208921 A208922

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 04 2012

STATUS

approved

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Last modified October 18 02:23 EDT 2019. Contains 328135 sequences. (Running on oeis4.)