A210199 Triangle of coefficients of polynomials u(n,x) jointly generated with A210200; see the Formula section.

1, 3, 6, 2, 11, 7, 2, 19, 19, 9, 2, 32, 44, 30, 11, 2, 53, 94, 83, 43, 13, 2, 87, 190, 207, 137, 58, 15, 2, 142, 370, 480, 387, 208, 75, 17, 2, 231, 701, 1057, 1004, 653, 298, 94, 19, 2, 375, 1301, 2238, 2448, 1865, 1026, 409, 115, 21, 2, 608, 2376, 4596

Offset

1,2

Comments

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

Links

Table of n, a(n) for n=1..59.

Formula

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

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
3
6....2
11...7....2
19...19...9...2
First three polynomials u(n,x): 1, 3, 6 + 2x.

Mathematica

u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := u[n - 1, x] + v[n - 1, x] + 1;
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[%]   (* A210199 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]  (* A210200 *)

Crossrefs

Cf. A210200, A208510.

Sequence in context: A210189 A257506 A210035 * A268717 A002516 A073807

Adjacent sequences: A210196 A210197 A210198 * A210200 A210201 A210202

Keyword

nonn,tabf

Author

Clark Kimberling, Mar 18 2012

Status

approved