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A208609 Triangle of coefficients of polynomials v(n,x) jointly generated with A208608; see the Formula section. 3
1, 2, 2, 2, 4, 3, 2, 6, 9, 5, 2, 8, 17, 18, 8, 2, 10, 27, 41, 35, 13, 2, 12, 39, 76, 93, 66, 21, 2, 14, 53, 125, 196, 200, 122, 34, 2, 16, 69, 190, 360, 472, 415, 222, 55, 2, 18, 87, 273, 603, 957, 1083, 837, 399, 89, 2, 20, 107, 376, 945, 1750, 2400, 2392 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

v(n,n)=Fibonacci(n+1)=A000045(n+1).

LINKS

Table of n, a(n) for n=1..63.

FORMULA

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

2...2

2...4...3

2...6...9....5

2...8...17...18...8

First five polynomials v(n,x):

1

2 + 2x

2 + 4x + 3x^2

2 + 6x + 9x^2 + 5x^3

2 + 8x + 17x^2 + 18x^3 + 8x^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_] := (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[%]  (* A208608 *)

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

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

TableForm[cv]

Flatten[%]  (* A208609 *)

CROSSREFS

Cf. A208608.

Sequence in context: A283681 A222819 A194319 * A249030 A257126 A050493

Adjacent sequences:  A208606 A208607 A208608 * A208610 A208611 A208612

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Feb 29 2012

STATUS

approved

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Last modified October 23 23:51 EDT 2019. Contains 328379 sequences. (Running on oeis4.)