A208607 Triangle of coefficients of polynomials v(n,x) jointly generated with A208606; see the Formula section.

1, 3, 1, 5, 3, 1, 7, 8, 6, 1, 9, 18, 19, 6, 1, 11, 35, 47, 25, 9, 1, 13, 61, 102, 81, 42, 9, 1, 15, 98, 203, 219, 147, 51, 12, 1, 17, 148, 378, 520, 435, 216, 74, 12, 1, 19, 213, 666, 1122, 1145, 747, 334, 86, 15, 1, 21, 295, 1119, 2250, 2753, 2233, 1245, 450

Offset: 1

Author

Clark Kimberling, Feb 29 2012

Keywords

• nonn
• tabl

Comments

Alternating rows sums: 1,2,3,4,5,6,7,8,...

Examples

			First five rows:
1
3...1
5...3...1
7...8...6...1
9...18...19...6...1
First five polynomials v(n,x):
1
3 + x
5 + 3x + x^2
7 + 8x + 6x^2 + x^3
9 + 18x + 19x^2 + 6x^3 + x^4
		

Crossrefs

Cf. A208606.

Programs

Mathematica

u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := u[n - 1, x] + x*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[%]  (* A208606 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]  (* A208607 *)

Formula

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