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A209702 Triangle of coefficients of polynomials v(n,x) jointly generated with A209701; see the Formula section. 3
1, 2, 3, 3, 5, 7, 4, 8, 16, 17, 5, 12, 30, 47, 41, 6, 17, 50, 99, 134, 99, 7, 23, 77, 181, 315, 373, 239, 8, 30, 112, 302, 628, 968, 1020, 577, 9, 38, 156, 472, 1128, 2090, 2898, 2751, 1393, 10, 47, 210, 702, 1882, 4020, 6738, 8495, 7338, 3363, 11, 57 (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..57.

FORMULA

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

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

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

EXAMPLE

First five rows:

1

2...3

3...5....7

4...8....16...17

5...12...30...57...41

First three polynomials v(n,x): 1, 2 + 3x , 3 + 5x + 7x^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] + (x + 1)*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[%]  (* A209701 *)

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

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

TableForm[cv]

Flatten[%]  (* A209702 *)

CROSSREFS

Cf. A209701, A208510.

Sequence in context: A092557 A144680 A081493 * A077558 A122444 A066072

Adjacent sequences:  A209699 A209700 A209701 * A209703 A209704 A209705

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 12 2012

STATUS

approved

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