A210862 Triangle of coefficients of polynomials u(n,x) jointly generated with A210863; see the Formula section.

1, 2, 1, 3, 2, 2, 4, 6, 7, 3, 5, 15, 20, 16, 5, 6, 31, 57, 63, 37, 8, 7, 56, 153, 215, 184, 81, 13, 8, 92, 370, 684, 771, 513, 171, 21, 9, 141, 805, 2028, 2898, 2603, 1354, 351, 34, 10, 205, 1598, 5515, 10084, 11582, 8319, 3415, 703, 55, 11, 286, 2940

Offset

1,2

Comments

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

Column 2: A056520

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

Links

Table of n, a(n) for n=1..58.

Formula

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

v(n,x)=(x+n-1)*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...2....2
4...6....7....3
5...15...20...16...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*v[n - 1, x] + 1;
v[n_, x_] := (x + n - 1)*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[%]   (* A210862 *)
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]   (* A210863 *)

Crossrefs

Cf. A210863, A208510.

Sequence in context: A120933 A209756 A210795 * A298675 A365383 A144154

Adjacent sequences: A210859 A210860 A210861 * A210863 A210864 A210865

Keyword

nonn,tabl

Author

Clark Kimberling, Mar 28 2012

Status

approved