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A209158 Triangle of coefficients of polynomials u(n,x) jointly generated with A209159; see the Formula section. 3
1, 2, 1, 3, 5, 3, 4, 11, 13, 5, 5, 19, 35, 31, 11, 6, 29, 73, 101, 73, 21, 7, 41, 131, 247, 275, 167, 43, 8, 55, 213, 509, 769, 717, 377, 85, 9, 71, 323, 935, 1787, 2255, 1811, 839, 171, 10, 89, 465, 1581, 3657, 5829, 6321, 4461, 1849, 341, 11, 109, 643 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Alternating row sums: 1,1,1,1,1,1,1,1,1,1,1,1,1,1,...

For a discussion and guide to related arrays, see A208510.

LINKS

Table of n, a(n) for n=1..58.

FORMULA

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

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

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

EXAMPLE

First five rows:

1

2...1

3...5....5

4...11...13...5

5...19...35...31...11

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

MATHEMATICA

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

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

v[n_, x_] := 2 x*u[n - 1, x] + 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[%]    (* A209158 *)

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

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

TableForm[cv]

Flatten[%]    (* A209159 *)

CROSSREFS

Cf. A209159, A208510.

Sequence in context: A060083 A069931 A209152 * A209135 A258236 A258244

Adjacent sequences:  A209155 A209156 A209157 * A209159 A209160 A209161

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 07 2012

STATUS

approved

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Last modified October 17 16:51 EDT 2019. Contains 328120 sequences. (Running on oeis4.)