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A209582 Triangle of coefficients of polynomials v(n,x) jointly generated with A209581; see the Formula section. 3
1, 2, 3, 2, 6, 7, 3, 10, 17, 15, 3, 16, 39, 46, 31, 4, 21, 69, 129, 119, 63, 4, 30, 112, 260, 386, 296, 127, 5, 36, 172, 492, 890, 1082, 713, 255, 5, 48, 242, 828, 1898, 2832, 2897, 1674, 511, 6, 55, 342, 1318, 3522, 6682, 8511, 7495, 3851, 1023, 6, 70 (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..57.

FORMULA

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

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

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

EXAMPLE

First five rows:

1

2...3

2...6....7

3...10...17...15

3...16...39...46...31

First three polynomials v(n,x): 1, 2 + 3x , 2 + 6x + 7x^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] + 2 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[%]   (* A209581 *)

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

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

TableForm[cv]

Flatten[%]   (* A209582 *)

CROSSREFS

Cf. A209581, A208510.

Sequence in context: A306156 A276125 A208611 * A158279 A153984 A025502

Adjacent sequences:  A209579 A209580 A209581 * A209583 A209584 A209585

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 11 2012

STATUS

approved

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Last modified October 16 08:15 EDT 2019. Contains 328051 sequences. (Running on oeis4.)