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

1, 2, 2, 6, 7, 3, 16, 30, 20, 5, 50, 116, 108, 47, 8, 156, 460, 552, 338, 105, 13, 532, 1842, 2692, 2119, 941, 221, 21, 1856, 7532, 13072, 12574, 7216, 2452, 451, 34, 6876, 31600, 63240, 71860, 50525, 22371, 6035, 895, 55, 26200, 135576, 308568

Offset

1,2

Comments

Row n ends with F(n+1), where F=A000045 (Fibonacci numbers).

Column 1: A013989

Alternating row sums: 1,0,2,1,3,2,4,3,5,4,...

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

Links

Table of n, a(n) for n=1..48.

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....2
6....7.....3
16...30....20....5
50...116...108...47...8
First three polynomials v(n,x): 1, 2 + 2x, 6 + 7x + 3x^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. A210860, A208510.

Sequence in context: A305295 A174789 A210865 * A062073 A021445 A011145

Adjacent sequences: A210858 A210859 A210860 * A210862 A210863 A210864

Keyword

nonn,tabl

Author

Clark Kimberling, Mar 28 2012

Status

approved