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

1, 2, 2, 6, 7, 3, 12, 21, 18, 5, 20, 61, 75, 42, 8, 30, 151, 262, 231, 93, 13, 42, 323, 829, 1025, 656, 196, 21, 56, 617, 2330, 3935, 3607, 1742, 401, 34, 72, 1081, 5815, 13578, 16849, 11723, 4380, 799, 55, 90, 1771, 13070, 42167, 69475, 65727

Offset

1,2

Comments

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

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

Links

Table of n, a(n) for n=1..51.

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....2
6....7....3
12...21...18...5
20...61...75...34...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*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. A210864, A208510.

Sequence in context: A247525 A305295 A174789 * A210861 A062073 A021445

Adjacent sequences: A210862 A210863 A210864 * A210866 A210867 A210868

Keyword

nonn,tabl

Author

Clark Kimberling, Mar 28 2012

Status

approved