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

1, 2, 1, 4, 6, 3, 7, 18, 17, 5, 11, 42, 63, 42, 11, 16, 85, 183, 195, 103, 21, 22, 156, 452, 678, 558, 240, 43, 29, 266, 994, 1966, 2252, 1510, 553, 85, 37, 428, 2002, 5012, 7494, 6946, 3929, 1246, 171, 46, 657, 3762, 11586, 21702, 26060, 20265, 9909

Offset

1,2

Comments

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

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....1
4....6....3
7....18...17...5
11...42...63...42...11
First three polynomials v(n,x): 1, 2 + x, 4 + 6x + 3x^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. A209163, A208510.

Sequence in context: A180405 A171007 A209168 * A127366 A064786 A367286

Adjacent sequences: A209159 A209160 A209161 * A209163 A209164 A209165

Keyword

nonn,tabl

Author

Clark Kimberling, Mar 07 2012

Status

approved