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A209576 Triangle of coefficients of polynomials v(n,x) jointly generated with A209575; see the Formula section. 3
1, 1, 4, 1, 4, 10, 1, 4, 18, 22, 1, 4, 18, 66, 46, 1, 4, 18, 82, 206, 94, 1, 4, 18, 82, 342, 578, 190, 1, 4, 18, 82, 374, 1274, 1510, 382, 1, 4, 18, 82, 374, 1642, 4294, 3754, 766, 1, 4, 18, 82, 374, 1706, 6726, 13354, 9006, 1534, 1, 4, 18, 82, 374, 1706 (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..61.

FORMULA

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

v(n,x)=2x*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...4

1...4...10

1...4...18...22

1...4...18...66...46

First three polynomials v(n,x): 1, 1+4x, 1+4x+10x^2.

MATHEMATICA

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

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

v[n_, x_] := 2 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[%]   (* A209575 *)

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

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

TableForm[cv]

Flatten[%]   (* A209576 *)

CROSSREFS

Cf. A209575, A208510.

Sequence in context: A165487 A201286 A208527 * A055886 A132478 A208918

Adjacent sequences:  A209573 A209574 A209575 * A209577 A209578 A209579

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 11 2012

STATUS

approved

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Last modified October 15 22:25 EDT 2019. Contains 328038 sequences. (Running on oeis4.)