A209555 Triangle of coefficients of polynomials u(n,x) jointly generated with A209556; see the Formula section.

1, 1, 1, 2, 2, 1, 2, 5, 3, 1, 3, 6, 9, 4, 1, 3, 11, 13, 14, 5, 1, 4, 12, 28, 24, 20, 6, 1, 4, 19, 34, 59, 40, 27, 7, 1, 5, 20, 62, 80, 110, 62, 35, 8, 1, 5, 29, 70, 164, 166, 188, 91, 44, 9, 1, 6, 30, 115, 200, 376, 314, 301, 128, 54, 10, 1, 6, 41, 125, 365, 496, 776

Offset

1,4

Comments

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

Links

Table of n, a(n) for n=1..72.

Formula

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

v(n,x)=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...2...1
2...5...3...1
3...6...9...4...1
First three polynomials v(n,x): 1, 1 + x, 2 + 2x + 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_] := 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[%]    (* A209555 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]    (* A209556 *)

Crossrefs

Cf. A209556, A208510.

Sequence in context: A172021 A325182 A215959 * A059594 A183760 A125678

Adjacent sequences: A209552 A209553 A209554 * A209556 A209557 A209558

Keyword

nonn,tabl

Author

Clark Kimberling, Mar 10 2012

Status

approved