A207630 Triangle of coefficients of polynomials v(n,x) jointly generated with A207629; see the Formula section.

1, 3, 1, 6, 3, 12, 9, 1, 24, 24, 5, 48, 60, 19, 1, 96, 144, 62, 7, 192, 336, 184, 33, 1, 384, 768, 512, 128, 9, 768, 1728, 1360, 440, 51, 1, 1536, 3840, 3488, 1392, 230, 11, 3072, 8448, 8704, 4144, 900, 73, 1, 6144, 18432, 21248, 11776, 3192, 376, 13

Offset

1,2

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)=(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
3....1
6....3
12...9....1
24...24...5

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_] := (x + 1)*u[n - 1, x] + 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[%]  (* A207629 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]  (* A207630 *)

Crossrefs

Cf. A207629.

Sequence in context: A165188 A294778 A132180 * A368376 A126191 A070883

Adjacent sequences: A207627 A207628 A207629 * A207631 A207632 A207633

Keyword

nonn,tabf

Author

Clark Kimberling, Feb 23 2012

Status

approved