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

1, 1, 2, 4, 5, 3, 9, 13, 13, 5, 16, 37, 47, 32, 8, 25, 96, 152, 147, 73, 13, 36, 217, 469, 587, 432, 158, 21, 49, 435, 1344, 2127, 2090, 1183, 330, 34, 64, 793, 3487, 7186, 8979, 6965, 3064, 669, 55, 81, 1342, 8179, 22544, 35296, 35304, 21754, 7577

Offset

1,3

Comments

For n>1, row n starts with (n-1)^2 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..53.

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
1....2
4....5....3
9....13...13...5
16...37...47...32...8
First three polynomials v(n,x): 1, 1 + 2x, 4 + 5x + 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 - 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. A210862, A208510.

Sequence in context: A097292 A269780 A038776 * A245816 A118461 A332667

Adjacent sequences: A210860 A210861 A210862 * A210864 A210865 A210866

Keyword

nonn,tabl

Author

Clark Kimberling, Mar 28 2012

Status

approved