A208922 Triangle of coefficients of polynomials v(n,x) jointly generated with A208921; see the Formula section.

1, 3, 1, 5, 4, 2, 7, 13, 12, 2, 9, 32, 40, 16, 4, 11, 65, 108, 80, 36, 4, 13, 116, 258, 288, 180, 48, 8, 15, 189, 560, 842, 700, 324, 96, 8, 17, 288, 1120, 2144, 2312, 1536, 640, 128, 16, 19, 417, 2088, 4944, 6728, 5832, 3232, 1088, 240, 16, 21, 580, 3666

Offset: 1

Author

Clark Kimberling, Mar 04 2012

Keywords

• nonn
• tabl

Comments

Alternating row sums: 1,2,3,4,5,6,7,8,9,10,...

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

Examples

			First five rows:
1
3...1
5...4....2
7...13...12...2
9...32...40...16...4
First five polynomials v(n,x):
1
3 + x
5 + 4x + 2x^2
7 + 13x + 12x^2 + 2x^3
9 + 32x + 40x^2 + 16x^3 + 4x^4
		

Crossrefs

Cf. A208921, A208510.

Programs

Mathematica

u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := u[n - 1, x] + 2x*v[n - 1, x];
v[n_, x_] := (x + 1)*u[n - 1, x] + v[n - 1, x] + 1;
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[%]    (* A208921 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]    (* A208922 *)

Formula

u(n,x)=u(n-1,x)+2x*v(n-1,x),

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

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