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A210226 Triangle of coefficients of polynomials v(n,x) jointly generated with A210225; see the Formula section. 4
1, 2, 3, 3, 9, 5, 4, 18, 24, 7, 5, 30, 66, 51, 9, 6, 45, 140, 189, 94, 11, 7, 63, 255, 505, 457, 157, 13, 8, 84, 420, 1110, 1516, 976, 244, 15, 9, 108, 644, 2142, 3986, 3960, 1896, 359, 17, 10, 135, 936, 3766, 8960, 12338, 9276, 3419, 506, 19, 11, 165 (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)+v(n-1,x)+1,

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...9....5

4...18...24...7

5...30...66...51...9

First three polynomials v(n,x): 1, 2 + 3x , 3 + 9x + 5x^2.

MATHEMATICA

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

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

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[%]     (* A210225 *)

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

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

TableForm[cv]

Flatten[%]     (* A210226 *)

CROSSREFS

Cf. A210225, A208510.

Sequence in context: A207626 A232324 A124931 * A209163 A124932 A248788

Adjacent sequences:  A210223 A210224 A210225 * A210227 A210228 A210229

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 20 2012

STATUS

approved

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Last modified October 19 04:40 EDT 2019. Contains 328211 sequences. (Running on oeis4.)