A207627 Triangle of coefficients of polynomials u(n,x) jointly generated with A207628; see the Formula section.

1, 2, 3, 4, 4, 10, 8, 5, 18, 28, 16, 6, 28, 64, 72, 32, 7, 40, 120, 200, 176, 64, 8, 54, 200, 440, 576, 416, 128, 9, 70, 308, 840, 1456, 1568, 960, 256, 10, 88, 448, 1456, 3136, 4480, 4096, 2176, 512, 11, 108, 624, 2352, 6048, 10752, 13056, 10368, 4864

Offset

1,2

Comments

Column n is divisible by 2^(n-1); row n ends with 2^(n-1).

Links

Table of n, a(n) for n=1..55.

Formula

u(n,x)=u(n-1,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.

The row sums =: 2, 7, 22, 67, ... are given by (5*3^n -1)/2 for n = 0, 1, 2, 3, ... . - Philippe Deléham, Feb 25 2012

Example

First five rows:
1
2
3...4
4...10...8
5...18...28...16

Mathematica

u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := u[n - 1, x] + v[n - 1, x]
v[n_, x_] := 2 x*u[n - 1, x] + (x + 1)*v[n - 1, x] + 1
Table[Factor[u[n, x]], {n, 1, z}]
Table[Factor[v[n, x]], {n, 1, z}]
cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
TableForm[cu]
Flatten[%]    (* A207625 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]    (* A207626 *)

Crossrefs

Cf. A207628.

Sequence in context: A118263 A217478 A279788 * A102539 A240220 A250229

Adjacent sequences: A207624 A207625 A207626 * A207628 A207629 A207630

Keyword

nonn,tabf

Author

Clark Kimberling, Feb 21 2012

Status

approved