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A209584 Triangle of coefficients of polynomials v(n,x) jointly generated with A209583; see the Formula section. 3
1, 3, 2, 5, 7, 3, 9, 18, 14, 4, 15, 42, 48, 25, 5, 25, 89, 137, 107, 41, 6, 41, 180, 348, 364, 212, 63, 7, 67, 350, 820, 1078, 844, 386, 92, 8, 109, 663, 1827, 2902, 2864, 1773, 659, 129, 9, 177, 1230, 3906, 7284, 8692, 6809, 3453, 1069, 175, 10, 287 (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..56.

FORMULA

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

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

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

EXAMPLE

First five rows:

1

3....1

5....7....3

9....18...14...4

15...42...48...25...5

First three polynomials v(n,x): 1, 3 + x , 5 + 7x + 3x^2.

MATHEMATICA

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

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

v[n_, x_] := (x + 1)*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[%]   (* A209583 *)

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

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

TableForm[cv]

Flatten[%]   (* A209584 *)

CROSSREFS

Cf. A209583, A208510.

Sequence in context: A125026 A130295 A208613 * A209140 A265903 A006369

Adjacent sequences:  A209581 A209582 A209583 * A209585 A209586 A209587

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 11 2012

STATUS

approved

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Last modified August 18 08:57 EDT 2019. Contains 326077 sequences. (Running on oeis4.)