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A210190 Triangle of coefficients of polynomials v(n,x) jointly generated with A210189; see the Formula section. 3
1, 2, 2, 3, 8, 4, 20, 4, 5, 40, 24, 6, 70, 84, 8, 7, 112, 224, 64, 8, 168, 504, 288, 16, 9, 240, 1008, 960, 160, 10, 330, 1848, 2640, 880, 32, 11, 440, 3168, 6336, 3520, 384, 12, 572, 5148, 13728, 11440, 2496, 64, 13, 728, 8008, 27456, 32032, 11648 (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..54.

FORMULA

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

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...8

4...20...4

5...40...24

First three polynomials v(n,x): 1, 2 + 2x , 3 + 8x.

MATHEMATICA

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

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

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[%]   (* A210189 *)

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

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

TableForm[cv]

Flatten[%]   (* A210190 *)

CROSSREFS

Cf. A210189, A208510.

Sequence in context: A220553 A176383 A100551 * A070267 A205374 A056762

Adjacent sequences:  A210187 A210188 A210189 * A210191 A210192 A210193

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 18 2012

STATUS

approved

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Last modified October 31 00:58 EDT 2014. Contains 248845 sequences.