A208613 Triangle of coefficients of polynomials v(n,x) jointly generated with A208612; see the Formula section.

1, 3, 2, 5, 7, 3, 7, 17, 16, 5, 9, 34, 51, 33, 8, 11, 60, 127, 129, 65, 13, 13, 97, 272, 386, 302, 124, 21, 15, 147, 525, 975, 1052, 666, 231, 34, 17, 212, 938, 2186, 3049, 2646, 1409, 423, 55, 19, 294, 1578, 4482, 7757, 8650, 6285, 2887, 764, 89, 21

Offset: 1

Author

Clark Kimberling, Mar 01 2012

Keywords

• nonn
• tabl

Comments

Alternating row sums: 1,1,1,1,1,1,1,1,1,1,1,...

Examples

			First five rows:
1
3...2
5...7....3
7...17...16...3
9...34...51...33...8
First five polynomials v(n,x):
1
3 + 2x
5 + 7x + 3x^2
7 + 17x + 16x^2 + 3x^3
9 + 34x + 51x^2 + 33x^3 + 8x^4
		

Crossrefs

Cf. A208612.

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] + (x + 1)*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[%]  (* A208612 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]  (* A208613 *)

Formula

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

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

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