A210233 Triangle of coefficients of polynomials u(n,x) jointly generated with A210234; see the Formula section.

1, 2, 1, 3, 5, 1, 4, 10, 12, 1, 5, 18, 30, 27, 1, 6, 27, 68, 83, 58, 1, 7, 39, 119, 225, 217, 121, 1, 8, 52, 200, 454, 680, 544, 248, 1, 9, 68, 300, 866, 1566, 1928, 1320, 503, 1, 10, 85, 440, 1450, 3332, 5014, 5216, 3121, 1014, 1, 11, 105, 605, 2350, 6182

Offset

1,2

Comments

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

Links

Table of n, a(n) for n=1..60.

Formula

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

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...1
3...5....1
4...10...12...1
5...18...30...27...1
First three polynomials u(n,x): 1, 2 + x, 3 + 5x + 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] + 1;
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[%]      (* A210233 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]      (* A210234 *)

Crossrefs

Cf. A210234, A208510.

Sequence in context: A030237 A210557 A118243 * A347667 A297582 A134081

Adjacent sequences: A210230 A210231 A210232 * A210234 A210235 A210236

Keyword

nonn,tabl

Author

Clark Kimberling, Mar 20 2012

Status

approved