A208921 Triangle of coefficients of polynomials u(n,x) jointly generated with A208922; see the Formula section.

1, 1, 2, 1, 8, 2, 1, 18, 10, 4, 1, 32, 36, 28, 4, 1, 50, 100, 108, 36, 8, 1, 72, 230, 324, 196, 80, 8, 1, 98, 462, 840, 772, 440, 104, 16, 1, 128, 840, 1960, 2456, 1840, 752, 208, 16, 1, 162, 1416, 4200, 6744, 6464, 3824, 1488, 272, 32, 1, 200, 2250, 8376

Offset

1,3

Comments

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

Links

Table of n, a(n) for n=1..59.

Formula

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

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

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

Example

First five rows:
1
1...2
1...8....2
1...18...10...4
1...32...36...28...4
First five polynomials u(n,x):
1
1 + 2x
1 + 8x + 2x^2
1 + 18x + 10x^2 + 4x^3
1 + 32x + 36x^2 + 28x^3 + 4x^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] + 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[%]    (* A208921 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]    (* A208922 *)

Crossrefs

Cf. A208922, A208510.

Sequence in context: A020778 A118961 A180956 * A208660 A367024 A114706

Adjacent sequences: A208918 A208919 A208920 * A208922 A208923 A208924

Keyword

nonn,tabl

Author

Clark Kimberling, Mar 04 2012

Status

approved