A209557 Triangle of coefficients of polynomials u(n,x) jointly generated with A209558; see the Formula section.

1, 1, 1, 2, 3, 1, 2, 7, 7, 1, 3, 9, 18, 15, 1, 3, 16, 30, 41, 31, 1, 4, 18, 60, 87, 88, 63, 1, 4, 28, 78, 189, 232, 183, 127, 1, 5, 30, 136, 285, 535, 585, 374, 255, 1, 5, 43, 160, 541, 931, 1410, 1418, 757, 511, 1, 6, 45, 255, 705, 1886, 2808, 3534, 3339, 1524

Offset

1,4

Comments

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)=u(n-1,x)+2x*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...7...7....1
3...9...18...15...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_] := 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[%]    (* A209557 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]    (* A209558 *)

Crossrefs

Cf. A209558, A208510.

Sequence in context: A109200 A158909 A199915 * A183759 A101477 A077887

Adjacent sequences: A209554 A209555 A209556 * A209558 A209559 A209560

Keyword

nonn,tabl

Author

Clark Kimberling, Mar 10 2012

Status

approved