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A209768 Triangle of coefficients of polynomials v(n,x) jointly generated with A209767; see the Formula section. 3
1, 2, 3, 3, 7, 7, 4, 14, 26, 17, 5, 24, 64, 83, 41, 6, 37, 130, 251, 250, 99, 7, 53, 233, 599, 899, 723, 239, 8, 72, 382, 1232, 2478, 3022, 2034, 577, 9, 94, 586, 2282, 5774, 9476, 9700, 5607, 1393, 10, 119, 854, 3908, 11952, 24734, 34152, 30063 (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..53.

FORMULA

u(n,x)=x*u(n-1,x)+(x+1)*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...14...26...17

5...24...64...83...41

First three polynomials v(n,x): 1, 2 + 3x , 3 + 7x + 7x^2.

MATHEMATICA

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

u[n_, x_] := x*u[n - 1, x] + (x + 1)*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[%]    (* A209767 *)

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

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

TableForm[cv]

Flatten[%]    (* A209768 *)

CROSSREFS

Cf. A209667, A208510.

Sequence in context: A210558 A208920 A210234 * A209169 A222294 A181850

Adjacent sequences:  A209765 A209766 A209767 * A209769 A209770 A209771

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 15 2012

STATUS

approved

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Last modified October 17 19:18 EDT 2019. Contains 328127 sequences. (Running on oeis4.)