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A209579 Triangle of coefficients of polynomials u(n,x) jointly generated with A209580; see the Formula section. 3
1, 1, 1, 2, 3, 1, 2, 6, 6, 1, 3, 9, 14, 10, 1, 3, 14, 28, 29, 15, 1, 4, 18, 48, 71, 55, 21, 1, 4, 25, 75, 139, 158, 97, 28, 1, 5, 30, 112, 251, 356, 321, 161, 36, 1, 5, 39, 156, 413, 724, 828, 609, 254, 45, 1, 6, 45, 215, 645, 1321, 1874, 1782, 1094, 384, 55, 1, 6 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

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

LINKS

Table of n, a(n) for n=1..67.

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

1...1

2...3....1

2...6....6....1

3...9....14...10...1

First three polynomials v(n,x): 1, 1 + x, 2 + 3x + x^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. A209580, A208510.

Sequence in context: A154948 A109091 A138507 * A205699 A109200 A158909

Adjacent sequences:  A209576 A209577 A209578 * A209580 A209581 A209582

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 11 2012

STATUS

approved

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Last modified October 22 17:39 EDT 2019. Contains 328319 sequences. (Running on oeis4.)