A210864 Triangle of coefficients of polynomials u(n,x) jointly generated with A210865; see the Formula section.

1, 2, 1, 3, 3, 2, 4, 9, 9, 3, 5, 21, 30, 21, 5, 6, 41, 91, 96, 47, 8, 7, 71, 242, 358, 278, 101, 13, 8, 113, 565, 1187, 1303, 757, 209, 21, 9, 169, 1182, 3517, 5238, 4364, 1951, 422, 34, 10, 241, 2263, 9332, 18816, 21213, 13674, 4802, 833, 55, 11, 331

Offset

1,2

Comments

Row n starts with n and ends with F(n), where F=A000045 (Fibonacci numbers).

Column 2: A064999

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

Links

Table of n, a(n) for n=1..57.

Formula

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

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

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

Example

First five rows:
1
2...1
3...3....2
4...9....9....3
5...21...30...21...5
First three polynomials u(n,x): 1, 2 + x, 3 + 3x + 2x^2.

Mathematica

u[1, x_] := 1; v[1, x_] := 1; z = 14;
u[n_, x_] := u[n - 1, x] + x*v[n - 1, x] + 1;
v[n_, x_] := (x + n)*u[n - 1, x] + x*v[n - 1, x];
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[%]   (* A210864 *)
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]   (* A210865 *)

Crossrefs

Cf. A210865, A208510.

Sequence in context: A133341 A111492 A319254 * A349550 A144305 A138635

Adjacent sequences: A210861 A210862 A210863 * A210865 A210866 A210867

Keyword

nonn,tabl

Author

Clark Kimberling, Mar 28 2012

Status

approved