A210226 Triangle of coefficients of polynomials v(n,x) jointly generated with A210225; see the Formula section.

1, 2, 3, 3, 9, 5, 4, 18, 24, 7, 5, 30, 66, 51, 9, 6, 45, 140, 189, 94, 11, 7, 63, 255, 505, 457, 157, 13, 8, 84, 420, 1110, 1516, 976, 244, 15, 9, 108, 644, 2142, 3986, 3960, 1896, 359, 17, 10, 135, 936, 3766, 8960, 12338, 9276, 3419, 506, 19, 11, 165

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)+1,

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

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

Example

First five rows:
1
2...3
3...9....5
4...18...24...7
5...30...66...51...9
First three polynomials v(n,x): 1, 2 + 3x , 3 + 9x + 5x^2.

Mathematica

u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := x*u[n - 1, x] + v[n - 1, x] + 1;
v[n_, x_] := 2 x*u[n - 1, x] + (x + 1)*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[%]     (* A210225 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]     (* A210226 *)

Crossrefs

Cf. A210225, A208510.

Sequence in context: A207626 A232324 A124931 * A209163 A124932 A248788

Adjacent sequences: A210223 A210224 A210225 * A210227 A210228 A210229

Keyword

nonn,tabl

Author

Clark Kimberling, Mar 20 2012

Status

approved