A209580 Triangle of coefficients of polynomials v(n,x) jointly generated with A209579; see the Formula section.

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

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