A210860 Triangle of coefficients of polynomials u(n,x) jointly generated with A210861; see the Formula section of A210861.

1, 2, 1, 4, 5, 2, 10, 18, 12, 3, 26, 64, 62, 28, 5, 76, 230, 286, 183, 60, 8, 232, 846, 1298, 1073, 503, 126, 13, 764, 3220, 5832, 5884, 3563, 1288, 255, 21, 2620, 12608, 26436, 31530, 23353, 10956, 3158, 506, 34, 9496, 51084, 121276, 166630

Offset

1,2

Comments

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

Column 1: A000085

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

Links

Table of n, a(n) for n=1..49.

Formula

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

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
   4    5    2
  10   18   12    3
  26   64   62   28    5
First three polynomials u(n,x): 1, 2 + x, 4 + 5x + 2x^2.

Mathematica

u[1, x_] := 1; v[1, x_] := 1; z = 14;
u[n_, x_] := u[n - 1, x] + (x + 1)*v[n - 1, x];
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[%]   (* A210860 *)
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]   (* A210861 *)

Crossrefs

Cf. A210861, A208510.

Sequence in context: A209141 A038719 A125751 * A099492 A359708 A144203

Adjacent sequences: A210857 A210858 A210859 * A210861 A210862 A210863

Keyword

nonn,tabl

Author

Clark Kimberling, Mar 28 2012

Extensions

Definition clarified by Alonso del Arte and Harvey P. Dale, Dec 17 2012

Status

approved