A210867 Triangle of coefficients of polynomials v(n,x) jointly generated with A210866; see the Formula section.

1, 2, 1, 3, 5, 2, 4, 15, 12, 3, 5, 34, 51, 28, 5, 6, 65, 170, 156, 60, 8, 7, 111, 465, 680, 438, 126, 13, 8, 175, 1092, 2465, 2411, 1145, 255, 21, 9, 260, 2282, 7623, 10968, 7805, 2854, 506, 34, 10, 369, 4356, 20608, 42735, 43440, 23509, 6813, 984, 55

Offset

1,2

Comments

For n>1, row n starts with n and ends with F(n), where F=A000045 (Fibonacci numbers).

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

Links

Table of n, a(n) for n=1..55.

Formula

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

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

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

Example

First five rows:
1
2...1
3...5....2
4...15...12...3
5...34...51...28...5
First three polynomials v(n,x): 1, 2 + x, 3 + 5x + 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];
v[n_, x_] := (x + n)*u[n - 1, x] + x*v[n - 1, x] - 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[%]   (* A210866 *)
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]   (* A210867 *)

Crossrefs

Cf. A210866, A208510.

Sequence in context: A081450 A248408 A210880 * A019588 A193953 A201377

Adjacent sequences: A210864 A210865 A210866 * A210868 A210869 A210870

Keyword

nonn,tabl

Author

Clark Kimberling, Mar 29 2012

Status

approved