A208931 Triangle of coefficients of polynomials u(n,x) jointly generated with A208932; see the Formula section.

1, 1, 2, 1, 8, 4, 1, 18, 20, 8, 1, 32, 64, 56, 16, 1, 50, 160, 224, 136, 32, 1, 72, 340, 680, 664, 328, 64, 1, 98, 644, 1736, 2416, 1872, 760, 128, 1, 128, 1120, 3920, 7264, 7856, 4984, 1736, 256, 1, 162, 1824, 8064, 19056, 26992, 23768, 12832, 3896

Offset

1,3

Comments

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

Links

Table of n, a(n) for n=1..54.

Formula

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

v(n,x)=(x+1)*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
1...2
1...8....4
1...18...20...8
1...32...64...56...16
First five polynomials u(n,x):
1
1 + 2x
1 + 8x + 4x^2
1 + 18x + 20x^2 + 8x^3
1 + 32x + 64x^2 + 56x^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 + 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[%]    (* A208931 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]    (* A208932 *)

Crossrefs

Cf. A208931, A208510.

Sequence in context: A099379 A234014 A367994 * A133214 A191935 A156365

Adjacent sequences: A208928 A208929 A208930 * A208932 A208933 A208934

Keyword

nonn,tabl

Author

Clark Kimberling, Mar 04 2012

Status

approved