A209143 Triangle of coefficients of polynomials u(n,x) jointly generated with A209144; see the Formula section.

1, 2, 1, 5, 4, 11, 11, 1, 23, 28, 6, 47, 68, 23, 1, 95, 160, 74, 8, 191, 368, 216, 39, 1, 383, 832, 592, 152, 10, 767, 1856, 1552, 520, 59, 1, 1535, 4096, 3936, 1632, 270, 12, 3071, 8960, 9728, 4816, 1060, 83, 1, 6143, 19456, 23552, 13568, 3752, 436

Offset: 1

Author

Clark Kimberling, Mar 06 2012

Keywords

• nonn
• tabf

Comments

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

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

Examples

			First five rows:
1
2....1
5....4
11...11...1
23...28...6
First three polynomials u(n,x):  1, 2 + x, 5 + 4x
		

Crossrefs

Cf. A209144, A208510.

Programs

Mathematica

u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := u[n - 1, x] + (x + 1)*v[n - 1, x];
v[n_, x_] := 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[%]    (* A209143 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]    (* A209144 *)

Formula

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

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

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