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A208516 Triangle of coefficients of polynomials u(n,x) jointly generated with A208517; see the Formula section. 3
1, 1, 1, 1, 2, 3, 1, 3, 6, 7, 1, 4, 9, 15, 17, 1, 5, 12, 24, 39, 41, 1, 6, 15, 34, 66, 100, 99, 1, 7, 18, 45, 98, 178, 256, 239, 1, 8, 21, 57, 135, 276, 478, 653, 577, 1, 9, 24, 70, 177, 395, 772, 1275, 1661, 1393, 1, 10, 27, 84, 224, 536, 1145, 2139, 3383, 4214 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,5

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)=x*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...1

1...2...3

1...3...6...7

1...4...9...15...17

First five polynomials u(n,x):

1

1 + x

1 + 2x + 3x^2

1 + 3x + 6x^2 + 7x^3

1 + 4x + 9x^2 + 15x^3 + 17x^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*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[%]  (* A208516 *)

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

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

TableForm[cv]

Flatten[%]  (* A208517 *)

CROSSREFS

Cf. A208517.

Sequence in context: A208522 A209569 A176850 * A111808 A247046 A081422

Adjacent sequences:  A208513 A208514 A208515 * A208517 A208518 A208519

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Feb 28 2012

STATUS

approved

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Last modified October 17 18:58 EDT 2019. Contains 328127 sequences. (Running on oeis4.)