A209163 Triangle of coefficients of polynomials v(n,x) jointly generated with A209162; see the Formula section.

1, 2, 3, 3, 9, 5, 4, 20, 26, 11, 5, 38, 82, 71, 21, 6, 65, 204, 279, 176, 43, 7, 103, 439, 849, 845, 425, 85, 8, 154, 854, 2192, 3050, 2386, 990, 171, 9, 220, 1540, 5034, 9174, 9940, 6396, 2267, 341, 10, 303, 2616, 10578, 24232, 34102, 30228, 16521

Offset

1,2

Comments

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

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

Links

Table of n, a(n) for n=1..53.

Formula

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

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

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

Example

First five rows:
1
2...3
3...9...5
4...20...26...11
5...38...82...71...21
First three polynomials v(n,x): 1, 2 + 3x, 3 + 9x + 5x^2.

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_] := 2 x*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[%]    (* A209162 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]    (* A209163 *)

Crossrefs

Cf. A209162, A208510.

Sequence in context: A232324 A124931 A210226 * A124932 A248788 A340914

Adjacent sequences: A209160 A209161 A209162 * A209164 A209165 A209166

Keyword

nonn,tabl

Author

Clark Kimberling, Mar 07 2012

Status

approved