A208526 Triangle of coefficients of polynomials u(n,x) jointly generated with A208527; see the Formula section.

1, 1, 1, 1, 2, 4, 1, 3, 8, 10, 1, 4, 12, 22, 28, 1, 5, 16, 36, 68, 76, 1, 6, 20, 52, 120, 200, 208, 1, 7, 24, 70, 184, 376, 592, 568, 1, 8, 28, 90, 260, 608, 1184, 1736, 1552, 1, 9, 32, 112, 348, 900, 2016, 3672, 5072, 4240, 1, 10, 36, 136, 448, 1256, 3120

Offset

1,5

Links

Table of n, a(n) for n=1..62.

Formula

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

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

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

Example

First five rows:
1
1...1
1...2...4
1...3...8....10
1...4...12...22...28
First five polynomials u(n,x):
1
1 + x
1 + 2x + 4x^2
1 + 3x + 8x^2 + 10x^3
1 + 4x + 12x^2 + 22x^3 + 28x^4

Mathematica

u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := u[n - 1, x] + x*v[n - 1, x];
v[n_, x_] := 2 x*u[n - 1, x] + 2 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[%]  (* A208526 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]  (* A208527 *)

Crossrefs

Cf. A208527.

Sequence in context: A272977 A230505 A366062 * A275895 A369292 A158613

Adjacent sequences: A208523 A208524 A208525 * A208527 A208528 A208529

Keyword

nonn,tabl

Author

Clark Kimberling, Feb 29 2012

Status

approved