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A209700 Triangle of coefficients of polynomials v(n,x) jointly generated with A209699; see the Formula section. 3
1, 2, 2, 3, 2, 4, 4, 2, 8, 8, 5, 2, 14, 16, 16, 6, 2, 22, 26, 40, 32, 7, 2, 32, 38, 78, 88, 64, 8, 2, 44, 52, 134, 178, 200, 128, 9, 2, 58, 68, 212, 310, 446, 440, 256, 10, 2, 74, 86, 316, 492, 846, 1042, 968, 512, 11, 2, 92, 106, 450, 732, 1452, 2062, 2462 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

For a discussion and guide to related arrays, see A208510.

LINKS

Table of n, a(n) for n=1..64.

FORMULA

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

v(n,x)=2x*u(n-1,x)+v(n-1,x)+1,

where u(1,x)=1, v(1,x)=1.

EXAMPLE

First five rows:

1

2...2

3...2...4

4...2...8....8

5...2...14...16...16

First three polynomials v(n,x): 1, 2 + 2x , 3 + 2x + 4x^2.

MATHEMATICA

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

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

v[n_, x_] := 2 x*u[n - 1, 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[%]   (* A209699 *)

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

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

TableForm[cv]

Flatten[%]   (* A209700 *)

CROSSREFS

Cf. A209699, A208510.

Sequence in context: A175012 A051693 A266470 * A115980 A088936 A049822

Adjacent sequences:  A209697 A209698 A209699 * A209701 A209702 A209703

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 12 2012

STATUS

approved

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Last modified October 14 05:08 EDT 2019. Contains 327995 sequences. (Running on oeis4.)