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A208920 Triangle of coefficients of polynomials v(n,x) jointly generated with A208919; see the Formula section. 3
1, 2, 3, 3, 7, 7, 4, 12, 26, 19, 5, 18, 62, 85, 47, 6, 25, 120, 235, 264, 123, 7, 33, 205, 515, 879, 803, 311, 8, 42, 322, 980, 2254, 3038, 2358, 803, 9, 52, 476, 1694, 4914, 8708, 10156, 6865, 2047, 10, 63, 672, 2730, 9576, 20958, 32640, 32877, 19588 (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)+2x*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...7....7

4...12...26...19

5...18...62...85...47

First five polynomials v(n,x):

1

2 + 3x

3 + 7x + 7x^2

4 + 12x + 26x^2 + 19x^3

5 + 18x + 62x^2 + 85x^3 + 47x^4

MATHEMATICA

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

u[n_, x_] := u[n - 1, x] + 2 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[%]    (* A208919 *)

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

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

TableForm[cv]

Flatten[%]    (* A208920 *)

CROSSREFS

Cf. A208919, A208510.

Sequence in context: A143444 A108346 A210558 * A210234 A209768 A209169

Adjacent sequences:  A208917 A208918 A208919 * A208921 A208922 A208923

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 04 2012

STATUS

approved

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Last modified October 18 02:23 EDT 2019. Contains 328135 sequences. (Running on oeis4.)