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A209580 Triangle of coefficients of polynomials v(n,x) jointly generated with A209579; see the Formula section. 3
1, 2, 2, 2, 4, 3, 3, 7, 8, 4, 3, 11, 19, 15, 5, 4, 15, 34, 43, 26, 6, 4, 21, 57, 91, 87, 42, 7, 5, 26, 87, 176, 217, 163, 64, 8, 5, 34, 126, 301, 473, 472, 288, 93, 9, 6, 40, 176, 489, 908, 1150, 954, 485, 130, 10, 6, 50, 235, 745, 1626, 2460, 2587, 1817, 784 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Alternating row sums:  1,0,1,0,1,0,1,0,1,0,...

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

LINKS

Table of n, a(n) for n=1..64.

FORMULA

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

v(n,x)=(x+1)*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...2

2...4....3

3...7....8....4

3...11...19...15...1

First three polynomials v(n,x): 1, 2 + 2x , 2 + 4x + 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*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[%]   (* A209579 *)

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

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

TableForm[cv]

Flatten[%]   (* A209580 *)

CROSSREFS

Cf. A209579, A208510.

Sequence in context: A085454 A083403 A114091 * A166008 A194291 A194323

Adjacent sequences:  A209577 A209578 A209579 * A209581 A209582 A209583

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 11 2012

STATUS

approved

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Last modified October 20 10:00 EDT 2019. Contains 328257 sequences. (Running on oeis4.)