A209772 Triangle of coefficients of polynomials v(n,x) jointly generated with A209771; see the Formula section.

1, 2, 2, 2, 5, 4, 3, 9, 14, 8, 3, 14, 32, 36, 16, 4, 20, 60, 100, 88, 32, 4, 27, 100, 220, 288, 208, 64, 5, 35, 154, 420, 728, 784, 480, 128, 5, 44, 224, 728, 1568, 2240, 2048, 1088, 256, 6, 54, 312, 1176, 3024, 5376, 6528, 5184, 2432, 512, 6, 65, 420

Offset

1,2

Comments

Alternating row sums: 1,0,1,0,1,0,1,0,...

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

Links

Table of n, a(n) for n=1..58.

Formula

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

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

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

Example

First five rows:
1
2...2
2...5....4
3...9....14...8
3...14...32...36...16
First three polynomials v(n,x): 1, 2 + 2x , 2 + 5x + 4x^2.

Mathematica

u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := x*u[n - 1, x] + (x + 1)*v[n - 1, x];
v[n_, x_] := (x + 1)*u[n - 1, x] + 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[%]    (* A209771 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]    (* A209772 *)

Crossrefs

Cf. A209671, A208510.

Sequence in context: A208512 A208908 A209558 * A370164 A147293 A134634

Adjacent sequences: A209769 A209770 A209771 * A209773 A209774 A209775

Keyword

nonn,tabl

Author

Clark Kimberling, Mar 15 2012

Status

approved