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A208909 Triangle of coefficients of polynomials u(n,x) jointly generated with A208930; see the Formula section. 3
1, 1, 2, 1, 6, 6, 1, 10, 20, 16, 1, 14, 42, 68, 44, 1, 18, 72, 172, 220, 120, 1, 22, 110, 344, 648, 696, 328, 1, 26, 156, 600, 1480, 2336, 2160, 896, 1, 30, 210, 956, 2900, 5984, 8128, 6608, 2448, 1, 34, 272, 1428, 5124, 12984, 23056, 27536, 19984 (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)=(x+1)*u(n-1,x)+2x*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...10...20...16

1...14...42...68...44

First five polynomials u(n,x):

1

1 + 2x

1 + 6x + 6x^2

1 + 10x + 20x^2 + 16x^3

1 + 14x + 42x^2 + 68x^3 + 44x^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 + 1)*u[n - 1, x] + 2 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[%]    (* A208909 *)

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

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

TableForm[cv]

Flatten[%]    (* A208930 *)

CROSSREFS

Cf. A208909, A208510.

Sequence in context: A213615 A049019 A133314 * A229565 A259477 A208919

Adjacent sequences:  A208906 A208907 A208908 * A208910 A208911 A208912

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 04 2012

STATUS

approved

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Last modified October 20 10:45 EDT 2019. Contains 328257 sequences. (Running on oeis4.)