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A208523 Triangle of coefficients of polynomials v(n,x) jointly generated with A208522; see the Formula section. 3
1, 1, 3, 1, 3, 5, 1, 3, 7, 11, 1, 3, 9, 19, 21, 1, 3, 11, 27, 43, 43, 1, 3, 13, 35, 69, 103, 85, 1, 3, 15, 43, 99, 183, 231, 171, 1, 3, 17, 51, 133, 283, 449, 523, 341, 1, 3, 19, 59, 171, 403, 747, 1107, 1155, 683, 1, 3, 21, 67, 213, 543, 1133, 1971, 2637, 2543 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Table of n, a(n) for n=1..65.

FORMULA

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

v(n,x)=2x*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...3

1...3...5

1...3...7...11

1...3...9...19...21

First five polynomials v(n,x):

1

1 + 3x

1 + 3x + 5x^2

1 + 3x + 7x^2 + 11x^3

1 + 3x + 9x^2 + 19x^3 + 21x^4

MATHEMATICA

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

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

v[n_, x_] := 2 x*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[%]    (* A208522 *)

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

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

TableForm[cv]

Flatten[%]    (* A208523 *)

CROSSREFS

Cf. A208522.

Sequence in context: A294966 A258208 A210952 * A209572 A134231 A225598

Adjacent sequences:  A208520 A208521 A208522 * A208524 A208525 A208526

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Feb 29 2012

STATUS

approved

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Last modified October 22 22:34 EDT 2019. Contains 328335 sequences. (Running on oeis4.)