A208923 Triangle of coefficients of polynomials u(n,x) jointly generated with A208908; see the Formula section.

1, 1, 2, 1, 6, 4, 1, 10, 14, 8, 1, 14, 32, 38, 16, 1, 18, 58, 104, 90, 32, 1, 22, 92, 222, 296, 214, 64, 1, 26, 134, 408, 738, 808, 490, 128, 1, 30, 184, 678, 1552, 2286, 2104, 1110, 256, 1, 34, 242, 1048, 2906, 5392, 6674, 5320, 2474, 512, 1, 38, 308

Offset

1,3

Comments

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

Links

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

Formula

u(n,x)=u(n-1,x)+2x*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
1...2
1...6....4
1...10...14...8
1...14...32...38...16
First five polynomials u(n,x):
1
1 + 2x
1 + 6x + 4x^2
1 + 10x + 14x^2 + 8x^3
1 + 14x + 32x^2 + 38x^3 + 16x^4

Mathematica

u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := u[n - 1, x] + 2 x*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[%]    (* A208923 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]    (* A208908 *)

Crossrefs

Cf. A208908, A208510.

Sequence in context: A293409 A051482 A349573 * A185045 A208913 A208911

Adjacent sequences: A208920 A208921 A208922 * A208924 A208925 A208926

Keyword

nonn,tabl

Author

Clark Kimberling, Mar 04 2012

Status

approved