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

Author

Clark Kimberling, Mar 28 2012

Keywords

• nonn
• tabl

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.

Examples

			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
		

Crossrefs

Cf. A210860, A208510.

Programs

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 *)

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.